[{"publisher":"IOP Publishing","date_updated":"2024-04-07T12:56:40Z","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2024-04-07T12:56:35Z","volume":36,"title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","doi":"10.1088/1361-6544/ace22e","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"issue":"8","year":"2023","citation":{"chicago":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” <i>Nonlinearity</i> 36, no. 8 (2023): 4438–69. <a href=\"https://doi.org/10.1088/1361-6544/ace22e\">https://doi.org/10.1088/1361-6544/ace22e</a>.","ieee":"M. Winkler, “Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction,” <i>Nonlinearity</i>, vol. 36, no. 8, pp. 4438–4469, 2023, doi: <a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>.","ama":"Winkler M. Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. <i>Nonlinearity</i>. 2023;36(8):4438-4469. doi:<a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>","mla":"Winkler, Michael. “Stabilization despite Pervasive Strong Cross-Degeneracies in a Nonlinear Diffusion Model for Migration–Consumption Interaction.” <i>Nonlinearity</i>, vol. 36, no. 8, IOP Publishing, 2023, pp. 4438–69, doi:<a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>.","bibtex":"@article{Winkler_2023, title={Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}, volume={36}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/ace22e\">10.1088/1361-6544/ace22e</a>}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler, Michael}, year={2023}, pages={4438–4469} }","short":"M. Winkler, Nonlinearity 36 (2023) 4438–4469.","apa":"Winkler, M. (2023). Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction. <i>Nonlinearity</i>, <i>36</i>(8), 4438–4469. <a href=\"https://doi.org/10.1088/1361-6544/ace22e\">https://doi.org/10.1088/1361-6544/ace22e</a>"},"page":"4438-4469","intvolume":"        36","_id":"53345","user_id":"31496","keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Nonlinearity","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>A no-flux initial-boundary value problem for<jats:disp-formula id=\"nonace22eueqn1\"><jats:tex-math><?CDATA \\begin{align*} \\begin{cases} u_t = \\Delta \\big(u\\phi(v)\\big), \\\\[1mm] v_t = \\Delta v-uv, \\end{cases} \\qquad \\qquad (\\star) \\end{align*}?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" overflow=\"scroll\"><mml:mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em\" rowspacing=\"3pt\"><mml:mtr><mml:mtd><mml:mfenced close=\"\" open=\"{\"><mml:mtable columnalign=\"left left\" columnspacing=\"1em\" rowspacing=\".1em\"><mml:mtr><mml:mtd><mml:msub><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:mi>ϕ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>v</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mi>v</mml:mi><mml:mo>−</mml:mo><mml:mi>u</mml:mi><mml:mi>v</mml:mi><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>⋆</mml:mo><mml:mo stretchy=\"false\">)</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math><jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" orientation=\"portrait\" position=\"float\" xlink:href=\"nonace22eueqn1.gif\" xlink:type=\"simple\" /></jats:disp-formula>is considered in smoothly bounded subdomains of<jats:inline-formula><jats:tex-math><?CDATA $\\mathbb{R}^n$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn1.gif\" xlink:type=\"simple\" /></jats:inline-formula>with<jats:inline-formula><jats:tex-math><?CDATA $n\\geqslant 1$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>n</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn2.gif\" xlink:type=\"simple\" /></jats:inline-formula>and suitably regular initial data, where<jats:italic>φ</jats:italic>is assumed to reflect algebraic type cross-degeneracies by sharing essential features with<jats:inline-formula><jats:tex-math><?CDATA $0\\leqslant \\xi\\mapsto \\xi^\\alpha$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mn>0</mml:mn><mml:mo>⩽</mml:mo><mml:mi>ξ</mml:mi><mml:mo stretchy=\"false\">↦</mml:mo><mml:msup><mml:mi>ξ</mml:mi><mml:mi>α</mml:mi></mml:msup></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn3.gif\" xlink:type=\"simple\" /></jats:inline-formula>for some<jats:inline-formula><jats:tex-math><?CDATA $\\alpha\\geqslant 1$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>α</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn4.gif\" xlink:type=\"simple\" /></jats:inline-formula>. Based on the discovery of a gradient structure acting at regularity levels mild enough to be consistent with degeneracy-driven limitations of smoothness information, in this general setting it is shown that with some measurable limit profile<jats:inline-formula><jats:tex-math><?CDATA $u_\\infty$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:msub></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn5.gif\" xlink:type=\"simple\" /></jats:inline-formula>and some null set<jats:inline-formula><jats:tex-math><?CDATA $N_\\star\\subset (0,\\infty)$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:msub><mml:mi>N</mml:mi><mml:mo>⋆</mml:mo></mml:msub><mml:mo>⊂</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn6.gif\" xlink:type=\"simple\" /></jats:inline-formula>, a corresponding global generalized solution, known to exist according to recent literature, satisfies<jats:disp-formula id=\"nonace22eueqn2\"><jats:tex-math><?CDATA \\begin{align*} \\rho(u(\\cdot,t))\\stackrel{\\star}{\\rightharpoonup} \\rho(u_\\infty) \\quad \\textrm{in } L^\\infty(\\Omega) \\quad\\;\\; \\textrm{ and } \\quad\\;\\; v(\\cdot,t)\\to 0 \\quad \\textrm{in } L^p(\\Omega)\\; \\textrm{for all } p\\geqslant 1 \\end{align*}?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"block\" overflow=\"scroll\"><mml:mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em\" rowspacing=\"3pt\"><mml:mtr><mml:mtd><mml:mi>ρ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>u</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>⋅</mml:mo><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mover><mml:mrow><mml:mo stretchy=\"false\">⇀</mml:mo></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mi>ρ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mtext>in </mml:mtext></mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"normal\">Ω</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mtext> and </mml:mtext></mml:mrow><mml:mi>v</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>⋅</mml:mo><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mtext>in </mml:mtext></mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"normal\">Ω</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mtext>for all </mml:mtext></mml:mrow><mml:mi>p</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:math><jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" orientation=\"portrait\" position=\"float\" xlink:href=\"nonace22eueqn2.gif\" xlink:type=\"simple\" /></jats:disp-formula>as<jats:inline-formula><jats:tex-math><?CDATA $(0,\\infty)\\setminus N_\\star \\ni t\\to \\infty$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>∖</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mo>⋆</mml:mo></mml:msub><mml:mo>∋</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn7.gif\" xlink:type=\"simple\" /></jats:inline-formula>, where<jats:inline-formula><jats:tex-math><?CDATA $\\rho(\\xi): = \\frac{\\xi^2}{(\\xi+1)^2}$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>ρ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ξ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>:=</mml:mo><mml:mfrac><mml:msup><mml:mi>ξ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ξ</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mfrac></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn8.gif\" xlink:type=\"simple\" /></jats:inline-formula>,<jats:inline-formula><jats:tex-math><?CDATA $\\xi\\geqslant 0$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>ξ</mml:mi><mml:mo>⩾</mml:mo><mml:mn>0</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn9.gif\" xlink:type=\"simple\" /></jats:inline-formula>. In the particular case when either<jats:inline-formula><jats:tex-math><?CDATA $n\\leqslant 2$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>n</mml:mi><mml:mo>⩽</mml:mo><mml:mn>2</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn10.gif\" xlink:type=\"simple\" /></jats:inline-formula>and<jats:inline-formula><jats:tex-math><?CDATA $\\alpha\\geqslant 1$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>α</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn11.gif\" xlink:type=\"simple\" /></jats:inline-formula>is arbitrary, or<jats:inline-formula><jats:tex-math><?CDATA $n\\geqslant 1$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>n</mml:mi><mml:mo>⩾</mml:mo><mml:mn>1</mml:mn></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn12.gif\" xlink:type=\"simple\" /></jats:inline-formula>and<jats:inline-formula><jats:tex-math><?CDATA $\\alpha\\in [1,2]$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn13.gif\" xlink:type=\"simple\" /></jats:inline-formula>, additional quantitative information on the deviation of trajectories from the initial data is derived. This is found to imply a lower estimate for the spatial oscillation of the respective first components throughout evolution, and moreover this is seen to entail that each of the uncountably many steady states<jats:inline-formula><jats:tex-math><?CDATA $(u_\\star,0)$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mo>⋆</mml:mo></mml:msub><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn14.gif\" xlink:type=\"simple\" /></jats:inline-formula>of (<jats:inline-formula><jats:tex-math><?CDATA $\\star$?></jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"><mml:mo>⋆</mml:mo></mml:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"nonace22eieqn15.gif\" xlink:type=\"simple\" /></jats:inline-formula>) is stable with respect to a suitably chosen norm topology.</jats:p>","lang":"eng"}],"status":"public"},{"issue":"2","publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","intvolume":"        25","page":"1607-1656","citation":{"ama":"Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>. 2023;25(2):1607-1656. doi:<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>","chicago":"Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i> 25, no. 2 (2023): 1607–56. <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">https://doi.org/10.1007/s00023-023-01379-x</a>.","ieee":"B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, pp. 1607–1656, 2023, doi: <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>.","mla":"Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>.","short":"B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.","bibtex":"@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>}, number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}, year={2023}, pages={1607–1656} }","apa":"Delarue, B., Schütte, P., &#38; Weich, T. (2023). Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>, <i>25</i>(2), 1607–1656. <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">https://doi.org/10.1007/s00023-023-01379-x</a>"},"year":"2023","volume":25,"date_created":"2024-04-11T12:30:14Z","author":[{"first_name":"Benjamin","full_name":"Delarue, Benjamin","id":"70575","last_name":"Delarue"},{"last_name":"Schütte","id":"50168","full_name":"Schütte, Philipp","first_name":"Philipp"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"}],"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-11T12:37:34Z","doi":"10.1007/s00023-023-01379-x","title":"Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models","publication":"Annales Henri Poincaré","type":"journal_article","status":"public","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.</jats:p>","lang":"eng"}],"department":[{"_id":"548"}],"user_id":"70575","_id":"53410","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"]},{"citation":{"ama":"Schwind B, Wu X, Tiemann M, Fabritius H-O. Broadband Mie scattering effects by structural features of setae from the Saharan silver ant Cataglyphis bombycina. <i>Journal of the Optical Society of America B</i>. 2023;40(3):B49-B58. doi:<a href=\"https://doi.org/10.1364/josab.474899\">10.1364/josab.474899</a>","chicago":"Schwind, Bertram, Xia Wu, Michael Tiemann, and Helge-Otto Fabritius. “Broadband Mie Scattering Effects by Structural Features of Setae from the Saharan Silver Ant Cataglyphis Bombycina.” <i>Journal of the Optical Society of America B</i> 40, no. 3 (2023): B49–58. <a href=\"https://doi.org/10.1364/josab.474899\">https://doi.org/10.1364/josab.474899</a>.","ieee":"B. Schwind, X. Wu, M. Tiemann, and H.-O. Fabritius, “Broadband Mie scattering effects by structural features of setae from the Saharan silver ant Cataglyphis bombycina,” <i>Journal of the Optical Society of America B</i>, vol. 40, no. 3, pp. B49–B58, 2023, doi: <a href=\"https://doi.org/10.1364/josab.474899\">10.1364/josab.474899</a>.","mla":"Schwind, Bertram, et al. “Broadband Mie Scattering Effects by Structural Features of Setae from the Saharan Silver Ant Cataglyphis Bombycina.” <i>Journal of the Optical Society of America B</i>, vol. 40, no. 3, Optica Publishing Group, 2023, pp. B49–58, doi:<a href=\"https://doi.org/10.1364/josab.474899\">10.1364/josab.474899</a>.","bibtex":"@article{Schwind_Wu_Tiemann_Fabritius_2023, title={Broadband Mie scattering effects by structural features of setae from the Saharan silver ant Cataglyphis bombycina}, volume={40}, DOI={<a href=\"https://doi.org/10.1364/josab.474899\">10.1364/josab.474899</a>}, number={3}, journal={Journal of the Optical Society of America B}, publisher={Optica Publishing Group}, author={Schwind, Bertram and Wu, Xia and Tiemann, Michael and Fabritius, Helge-Otto}, year={2023}, pages={B49–B58} }","short":"B. Schwind, X. Wu, M. Tiemann, H.-O. Fabritius, Journal of the Optical Society of America B 40 (2023) B49–B58.","apa":"Schwind, B., Wu, X., Tiemann, M., &#38; Fabritius, H.-O. (2023). Broadband Mie scattering effects by structural features of setae from the Saharan silver ant Cataglyphis bombycina. <i>Journal of the Optical Society of America B</i>, <i>40</i>(3), B49–B58. <a href=\"https://doi.org/10.1364/josab.474899\">https://doi.org/10.1364/josab.474899</a>"},"page":"B49 - B58","intvolume":"        40","publication_status":"published","publication_identifier":{"issn":["0740-3224","1520-8540"]},"doi":"10.1364/josab.474899","author":[{"last_name":"Schwind","full_name":"Schwind, Bertram","first_name":"Bertram"},{"full_name":"Wu, Xia","last_name":"Wu","first_name":"Xia"},{"first_name":"Michael","orcid":"0000-0003-1711-2722","last_name":"Tiemann","full_name":"Tiemann, Michael","id":"23547"},{"first_name":"Helge-Otto","full_name":"Fabritius, Helge-Otto","last_name":"Fabritius"}],"volume":40,"date_updated":"2024-05-22T14:29:39Z","status":"public","type":"journal_article","article_type":"original","user_id":"23547","department":[{"_id":"35"},{"_id":"2"},{"_id":"307"},{"_id":"230"}],"_id":"42679","year":"2023","issue":"3","quality_controlled":"1","title":"Broadband Mie scattering effects by structural features of setae from the Saharan silver ant Cataglyphis bombycina","date_created":"2023-03-02T17:48:38Z","publisher":"Optica Publishing Group","abstract":[{"text":"The Saharan desert ant Cataglyphis bombycina is densely covered with shiny silver setae (hair-like structures). Their appearance was explained by geometric optics and total internal reflection. The setae also increase the emissivity of the ant, as they form an effective medium. This work provides additional data on microstructural details of the setae that are used to simulate the scattering of an individual seta to explain their influence on the optical properties. This is achieved by characterization of their structure using light microscopy and scanning/transmission electron microscopy. How the microstructural features influence scattering is investigated wave-optically within the limits of finite-difference time-domain simulations from the ultraviolet to the mid-infrared spectral range to elucidate the optical effects beyond ray optics and effective medium theory. The results show that Mie scattering plays an important role in protecting the ant from solar radiation and could be relevant for its thermal tolerance.","lang":"eng"}],"publication":"Journal of the Optical Society of America B","language":[{"iso":"eng"}],"keyword":["Atomic and Molecular Physics","and Optics","Statistical and Nonlinear Physics"]},{"_id":"33264","user_id":"97359","extern":"1","type":"journal_article","status":"public","date_updated":"2022-09-07T08:36:46Z","volume":35,"author":[{"first_name":"Sören","id":"97359","full_name":"von der Gracht, Sören","last_name":"von der Gracht","orcid":"0000-0002-8054-2058"},{"last_name":"Nijholt","full_name":"Nijholt, Eddie","first_name":"Eddie"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"}],"doi":"10.1088/1361-6544/ac5463","publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","intvolume":"        35","page":"2073-2120","citation":{"apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (2022). Amplified steady state bifurcations in feedforward networks. <i>Nonlinearity</i>, <i>35</i>(4), 2073–2120. <a href=\"https://doi.org/10.1088/1361-6544/ac5463\">https://doi.org/10.1088/1361-6544/ac5463</a>","bibtex":"@article{von der Gracht_Nijholt_Rink_2022, title={Amplified steady state bifurcations in feedforward networks}, volume={35}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/ac5463\">10.1088/1361-6544/ac5463</a>}, number={4}, journal={Nonlinearity}, publisher={IOP Publishing}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2022}, pages={2073–2120} }","short":"S. von der Gracht, E. Nijholt, B. Rink, Nonlinearity 35 (2022) 2073–2120.","mla":"von der Gracht, Sören, et al. “Amplified Steady State Bifurcations in Feedforward Networks.” <i>Nonlinearity</i>, vol. 35, no. 4, IOP Publishing, 2022, pp. 2073–120, doi:<a href=\"https://doi.org/10.1088/1361-6544/ac5463\">10.1088/1361-6544/ac5463</a>.","ama":"von der Gracht S, Nijholt E, Rink B. Amplified steady state bifurcations in feedforward networks. <i>Nonlinearity</i>. 2022;35(4):2073-2120. doi:<a href=\"https://doi.org/10.1088/1361-6544/ac5463\">10.1088/1361-6544/ac5463</a>","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Amplified Steady State Bifurcations in Feedforward Networks.” <i>Nonlinearity</i> 35, no. 4 (2022): 2073–2120. <a href=\"https://doi.org/10.1088/1361-6544/ac5463\">https://doi.org/10.1088/1361-6544/ac5463</a>.","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Amplified steady state bifurcations in feedforward networks,” <i>Nonlinearity</i>, vol. 35, no. 4, pp. 2073–2120, 2022, doi: <a href=\"https://doi.org/10.1088/1361-6544/ac5463\">10.1088/1361-6544/ac5463</a>."},"external_id":{"arxiv":["2105.02547"]},"keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication":"Nonlinearity","abstract":[{"lang":"eng","text":"We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations for such networks. Branching solutions and their asymptotics are described in terms of Taylor coefficients of the internal dynamics. They can be determined via an algorithm that only exploits the network structure. Similar to previous results on feedforward chains, we observe amplifications of the growth rates of steady state branches induced by the feedforward structure. However, contrary to these earlier results, as the interaction scenarios can be more complicated in general feedforward networks, different branching patterns and different amplifications can occur for different regions in the space of Taylor coefficients."}],"publisher":"IOP Publishing","date_created":"2022-09-06T11:38:15Z","title":"Amplified steady state bifurcations in feedforward networks","issue":"4","year":"2022"},{"status":"public","type":"journal_article","publication":"Advanced Quantum Technologies","article_number":"2200049","keyword":["Electrical and Electronic Engineering","Computational Theory and Mathematics","Condensed Matter Physics","Mathematical Physics","Nuclear and High Energy Physics","Electronic","Optical and Magnetic Materials","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"_id":"33332","user_id":"42514","department":[{"_id":"15"},{"_id":"230"}],"year":"2022","citation":{"apa":"Bopp, F., Rojas, J., Revenga, N., Riedl, H., Sbresny, F., Boos, K., Simmet, T., Ahmadi, A., Gershoni, D., Kasprzak, J., Ludwig, A., Reitzenstein, S., Wieck, A., Reuter, D., Müller, K., &#38; Finley, J. J. (2022). Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling. <i>Advanced Quantum Technologies</i>, Article 2200049. <a href=\"https://doi.org/10.1002/qute.202200049\">https://doi.org/10.1002/qute.202200049</a>","bibtex":"@article{Bopp_Rojas_Revenga_Riedl_Sbresny_Boos_Simmet_Ahmadi_Gershoni_Kasprzak_et al._2022, title={Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling}, DOI={<a href=\"https://doi.org/10.1002/qute.202200049\">10.1002/qute.202200049</a>}, number={2200049}, journal={Advanced Quantum Technologies}, publisher={Wiley}, author={Bopp, Frederik and Rojas, Jonathan and Revenga, Natalia and Riedl, Hubert and Sbresny, Friedrich and Boos, Katarina and Simmet, Tobias and Ahmadi, Arash and Gershoni, David and Kasprzak, Jacek and et al.}, year={2022} }","mla":"Bopp, Frederik, et al. “Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling.” <i>Advanced Quantum Technologies</i>, 2200049, Wiley, 2022, doi:<a href=\"https://doi.org/10.1002/qute.202200049\">10.1002/qute.202200049</a>.","short":"F. Bopp, J. Rojas, N. Revenga, H. Riedl, F. Sbresny, K. Boos, T. Simmet, A. Ahmadi, D. Gershoni, J. Kasprzak, A. Ludwig, S. Reitzenstein, A. Wieck, D. Reuter, K. Müller, J.J. Finley, Advanced Quantum Technologies (2022).","chicago":"Bopp, Frederik, Jonathan Rojas, Natalia Revenga, Hubert Riedl, Friedrich Sbresny, Katarina Boos, Tobias Simmet, et al. “Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling.” <i>Advanced Quantum Technologies</i>, 2022. <a href=\"https://doi.org/10.1002/qute.202200049\">https://doi.org/10.1002/qute.202200049</a>.","ieee":"F. Bopp <i>et al.</i>, “Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling,” <i>Advanced Quantum Technologies</i>, Art. no. 2200049, 2022, doi: <a href=\"https://doi.org/10.1002/qute.202200049\">10.1002/qute.202200049</a>.","ama":"Bopp F, Rojas J, Revenga N, et al. Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling. <i>Advanced Quantum Technologies</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1002/qute.202200049\">10.1002/qute.202200049</a>"},"publication_status":"published","publication_identifier":{"issn":["2511-9044","2511-9044"]},"title":"Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling","doi":"10.1002/qute.202200049","date_updated":"2022-09-12T07:18:06Z","publisher":"Wiley","author":[{"full_name":"Bopp, Frederik","last_name":"Bopp","first_name":"Frederik"},{"last_name":"Rojas","full_name":"Rojas, Jonathan","first_name":"Jonathan"},{"first_name":"Natalia","last_name":"Revenga","full_name":"Revenga, Natalia"},{"first_name":"Hubert","last_name":"Riedl","full_name":"Riedl, Hubert"},{"last_name":"Sbresny","full_name":"Sbresny, Friedrich","first_name":"Friedrich"},{"last_name":"Boos","full_name":"Boos, Katarina","first_name":"Katarina"},{"last_name":"Simmet","full_name":"Simmet, Tobias","first_name":"Tobias"},{"full_name":"Ahmadi, Arash","last_name":"Ahmadi","first_name":"Arash"},{"first_name":"David","last_name":"Gershoni","full_name":"Gershoni, David"},{"first_name":"Jacek","full_name":"Kasprzak, Jacek","last_name":"Kasprzak"},{"full_name":"Ludwig, Arne","last_name":"Ludwig","first_name":"Arne"},{"full_name":"Reitzenstein, Stephan","last_name":"Reitzenstein","first_name":"Stephan"},{"first_name":"Andreas","full_name":"Wieck, Andreas","last_name":"Wieck"},{"last_name":"Reuter","full_name":"Reuter, Dirk","id":"37763","first_name":"Dirk"},{"last_name":"Müller","full_name":"Müller, Kai","first_name":"Kai"},{"first_name":"Jonathan J.","full_name":"Finley, Jonathan J.","last_name":"Finley"}],"date_created":"2022-09-12T07:17:26Z"},{"user_id":"49063","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"_id":"35322","language":[{"iso":"eng"}],"keyword":["Geometry and Topology","Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","publication":"Journal of Spectral Theory","status":"public","date_created":"2023-01-06T08:49:06Z","author":[{"first_name":"Kai-Uwe","full_name":"Bux, Kai-Uwe","last_name":"Bux"},{"first_name":"Joachim","last_name":"Hilgert","id":"220","full_name":"Hilgert, Joachim"},{"id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"}],"volume":12,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_updated":"2024-02-19T06:28:12Z","doi":"10.4171/jst/414","title":"Poisson transforms for trees of bounded degree","issue":"2","publication_status":"published","publication_identifier":{"issn":["1664-039X"]},"citation":{"ieee":"K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded degree,” <i>Journal of Spectral Theory</i>, vol. 12, no. 2, pp. 659–681, 2022, doi: <a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>.","chicago":"Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for Trees of Bounded Degree.” <i>Journal of Spectral Theory</i> 12, no. 2 (2022): 659–81. <a href=\"https://doi.org/10.4171/jst/414\">https://doi.org/10.4171/jst/414</a>.","ama":"Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree. <i>Journal of Spectral Theory</i>. 2022;12(2):659-681. doi:<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>","mla":"Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” <i>Journal of Spectral Theory</i>, vol. 12, no. 2, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 659–81, doi:<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>.","bibtex":"@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, DOI={<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>}, number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}, year={2022}, pages={659–681} }","short":"K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.","apa":"Bux, K.-U., Hilgert, J., &#38; Weich, T. (2022). Poisson transforms for trees of bounded degree. <i>Journal of Spectral Theory</i>, <i>12</i>(2), 659–681. <a href=\"https://doi.org/10.4171/jst/414\">https://doi.org/10.4171/jst/414</a>"},"page":"659-681","intvolume":"        12","year":"2022"},{"article_number":"033216","department":[{"_id":"27"}],"user_id":"15278","_id":"32243","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"status":"public","type":"journal_article","doi":"10.1088/1742-5468/abe6fd","volume":2021,"author":[{"last_name":"Dabelow","full_name":"Dabelow, Lennart","first_name":"Lennart"},{"full_name":"Bo, Stefano","last_name":"Bo","first_name":"Stefano"},{"first_name":"Ralf","last_name":"Eichhorn","full_name":"Eichhorn, Ralf"}],"date_updated":"2022-06-28T07:28:14Z","intvolume":"      2021","citation":{"apa":"Dabelow, L., Bo, S., &#38; Eichhorn, R. (2021). How irreversible are steady-state trajectories of a trapped active particle? <i>Journal of Statistical Mechanics: Theory and Experiment</i>, <i>2021</i>(3), Article 033216. <a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">https://doi.org/10.1088/1742-5468/abe6fd</a>","bibtex":"@article{Dabelow_Bo_Eichhorn_2021, title={How irreversible are steady-state trajectories of a trapped active particle?}, volume={2021}, DOI={<a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>}, number={3033216}, journal={Journal of Statistical Mechanics: Theory and Experiment}, publisher={IOP Publishing}, author={Dabelow, Lennart and Bo, Stefano and Eichhorn, Ralf}, year={2021} }","short":"L. Dabelow, S. Bo, R. Eichhorn, Journal of Statistical Mechanics: Theory and Experiment 2021 (2021).","mla":"Dabelow, Lennart, et al. “How Irreversible Are Steady-State Trajectories of a Trapped Active Particle?” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 3, 033216, IOP Publishing, 2021, doi:<a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>.","ama":"Dabelow L, Bo S, Eichhorn R. How irreversible are steady-state trajectories of a trapped active particle? <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2021;2021(3). doi:<a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>","ieee":"L. Dabelow, S. Bo, and R. Eichhorn, “How irreversible are steady-state trajectories of a trapped active particle?,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 3, Art. no. 033216, 2021, doi: <a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>.","chicago":"Dabelow, Lennart, Stefano Bo, and Ralf Eichhorn. “How Irreversible Are Steady-State Trajectories of a Trapped Active Particle?” <i>Journal of Statistical Mechanics: Theory and Experiment</i> 2021, no. 3 (2021). <a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">https://doi.org/10.1088/1742-5468/abe6fd</a>."},"publication_identifier":{"issn":["1742-5468"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability","Statistical and Nonlinear Physics"],"abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment (e.g. an aqueous solution), thus keeping them permanently out of equilibrium. Nevertheless, the spatial dynamics of active particles might share certain equilibrium features, in particular in the steady state. We here focus on the time-reversal symmetry of individual spatial trajectories as a distinct equilibrium characteristic. We investigate to what extent the steady-state trajectories of a trapped active particle obey or break this time-reversal symmetry. Within the framework of active Ornstein–Uhlenbeck particles we find that the steady-state trajectories in a harmonic potential fulfill path-wise time-reversal symmetry exactly, while this symmetry is typically broken in anharmonic potentials.</jats:p>","lang":"eng"}],"publication":"Journal of Statistical Mechanics: Theory and Experiment","title":"How irreversible are steady-state trajectories of a trapped active particle?","date_created":"2022-06-28T07:27:41Z","publisher":"IOP Publishing","year":"2021","issue":"3"},{"year":"2021","issue":"11","title":"Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds","publisher":"Springer Science and Business Media LLC","date_created":"2022-06-20T08:37:52Z","publication":"Annales Henri Poincaré","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"page":"3565-3617","intvolume":"        22","citation":{"apa":"Guillarmou, C., &#38; Küster, B. (2021). Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. <i>Annales Henri Poincaré</i>, <i>22</i>(11), 3565–3617. <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">https://doi.org/10.1007/s00023-021-01068-7</a>","bibtex":"@article{Guillarmou_Küster_2021, title={Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds}, volume={22}, DOI={<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>}, number={11}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Guillarmou, Colin and Küster, Benjamin}, year={2021}, pages={3565–3617} }","mla":"Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, Springer Science and Business Media LLC, 2021, pp. 3565–617, doi:<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>.","short":"C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617.","ieee":"C. Guillarmou and B. Küster, “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds,” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, pp. 3565–3617, 2021, doi: <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>.","chicago":"Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i> 22, no. 11 (2021): 3565–3617. <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">https://doi.org/10.1007/s00023-021-01068-7</a>.","ama":"Guillarmou C, Küster B. Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. <i>Annales Henri Poincaré</i>. 2021;22(11):3565-3617. doi:<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>"},"publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","doi":"10.1007/s00023-021-01068-7","date_updated":"2024-04-11T12:39:23Z","volume":22,"author":[{"first_name":"Colin","full_name":"Guillarmou, Colin","last_name":"Guillarmou"},{"first_name":"Benjamin","full_name":"Küster, Benjamin","last_name":"Küster"}],"status":"public","type":"journal_article","_id":"32006","department":[{"_id":"548"}],"user_id":"70575"},{"language":[{"iso":"eng"}],"article_number":"2100002","keyword":["Electrical and Electronic Engineering","Computational Theory and Mathematics","Condensed Matter Physics","Mathematical Physics","Nuclear and High Energy Physics","Electronic","Optical and Magnetic Materials","Statistical and Nonlinear Physics"],"user_id":"42514","department":[{"_id":"15"},{"_id":"230"}],"_id":"46135","status":"public","type":"journal_article","publication":"Advanced Quantum Technologies","doi":"10.1002/qute.202100002","title":"Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography","date_created":"2023-07-25T08:45:57Z","author":[{"first_name":"Johannes","full_name":"Schall, Johannes","last_name":"Schall"},{"last_name":"Deconinck","full_name":"Deconinck, Marielle","first_name":"Marielle"},{"first_name":"Nikolai","full_name":"Bart, Nikolai","last_name":"Bart"},{"full_name":"Florian, Matthias","last_name":"Florian","first_name":"Matthias"},{"full_name":"Helversen, Martin","last_name":"Helversen","first_name":"Martin"},{"last_name":"Dangel","full_name":"Dangel, Christian","first_name":"Christian"},{"first_name":"Ronny","last_name":"Schmidt","full_name":"Schmidt, Ronny"},{"first_name":"Lucas","full_name":"Bremer, Lucas","last_name":"Bremer"},{"first_name":"Frederik","full_name":"Bopp, Frederik","last_name":"Bopp"},{"last_name":"Hüllen","full_name":"Hüllen, Isabell","first_name":"Isabell"},{"full_name":"Gies, Christopher","last_name":"Gies","first_name":"Christopher"},{"first_name":"Dirk","id":"37763","full_name":"Reuter, Dirk","last_name":"Reuter"},{"full_name":"Wieck, Andreas D.","last_name":"Wieck","first_name":"Andreas D."},{"last_name":"Rodt","full_name":"Rodt, Sven","first_name":"Sven"},{"first_name":"Jonathan J.","full_name":"Finley, Jonathan J.","last_name":"Finley"},{"first_name":"Frank","last_name":"Jahnke","full_name":"Jahnke, Frank"},{"last_name":"Ludwig","full_name":"Ludwig, Arne","first_name":"Arne"},{"full_name":"Reitzenstein, Stephan","last_name":"Reitzenstein","first_name":"Stephan"}],"volume":4,"date_updated":"2023-07-25T08:46:47Z","publisher":"Wiley","citation":{"bibtex":"@article{Schall_Deconinck_Bart_Florian_Helversen_Dangel_Schmidt_Bremer_Bopp_Hüllen_et al._2021, title={Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography}, volume={4}, DOI={<a href=\"https://doi.org/10.1002/qute.202100002\">10.1002/qute.202100002</a>}, number={62100002}, journal={Advanced Quantum Technologies}, publisher={Wiley}, author={Schall, Johannes and Deconinck, Marielle and Bart, Nikolai and Florian, Matthias and Helversen, Martin and Dangel, Christian and Schmidt, Ronny and Bremer, Lucas and Bopp, Frederik and Hüllen, Isabell and et al.}, year={2021} }","short":"J. Schall, M. Deconinck, N. Bart, M. Florian, M. Helversen, C. Dangel, R. Schmidt, L. Bremer, F. Bopp, I. Hüllen, C. Gies, D. Reuter, A.D. Wieck, S. Rodt, J.J. Finley, F. Jahnke, A. Ludwig, S. Reitzenstein, Advanced Quantum Technologies 4 (2021).","mla":"Schall, Johannes, et al. “Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography.” <i>Advanced Quantum Technologies</i>, vol. 4, no. 6, 2100002, Wiley, 2021, doi:<a href=\"https://doi.org/10.1002/qute.202100002\">10.1002/qute.202100002</a>.","apa":"Schall, J., Deconinck, M., Bart, N., Florian, M., Helversen, M., Dangel, C., Schmidt, R., Bremer, L., Bopp, F., Hüllen, I., Gies, C., Reuter, D., Wieck, A. D., Rodt, S., Finley, J. J., Jahnke, F., Ludwig, A., &#38; Reitzenstein, S. (2021). Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography. <i>Advanced Quantum Technologies</i>, <i>4</i>(6), Article 2100002. <a href=\"https://doi.org/10.1002/qute.202100002\">https://doi.org/10.1002/qute.202100002</a>","chicago":"Schall, Johannes, Marielle Deconinck, Nikolai Bart, Matthias Florian, Martin Helversen, Christian Dangel, Ronny Schmidt, et al. “Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography.” <i>Advanced Quantum Technologies</i> 4, no. 6 (2021). <a href=\"https://doi.org/10.1002/qute.202100002\">https://doi.org/10.1002/qute.202100002</a>.","ieee":"J. Schall <i>et al.</i>, “Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography,” <i>Advanced Quantum Technologies</i>, vol. 4, no. 6, Art. no. 2100002, 2021, doi: <a href=\"https://doi.org/10.1002/qute.202100002\">10.1002/qute.202100002</a>.","ama":"Schall J, Deconinck M, Bart N, et al. Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography. <i>Advanced Quantum Technologies</i>. 2021;4(6). doi:<a href=\"https://doi.org/10.1002/qute.202100002\">10.1002/qute.202100002</a>"},"intvolume":"         4","year":"2021","issue":"6","publication_status":"published","publication_identifier":{"issn":["2511-9044","2511-9044"]}},{"language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publication":"Communications in Mathematical Physics","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n</jats:p>"}],"date_created":"2022-05-17T12:06:06Z","publisher":"Springer Science and Business Media LLC","title":"Pollicott-Ruelle Resonant States and Betti Numbers","issue":"2","year":"2020","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","_id":"31264","type":"journal_article","status":"public","volume":378,"author":[{"first_name":"Benjamin","full_name":"Küster, Benjamin","last_name":"Küster"},{"full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"}],"date_updated":"2022-05-19T10:13:48Z","doi":"10.1007/s00220-020-03793-2","publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","intvolume":"       378","page":"917-941","citation":{"mla":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, Springer Science and Business Media LLC, 2020, pp. 917–41, doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","bibtex":"@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias}, year={2020}, pages={917–941} }","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","apa":"Küster, B., &#38; Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>, <i>378</i>(2), 917–941. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>","chicago":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i> 378, no. 2 (2020): 917–41. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>.","ieee":"B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, pp. 917–941, 2020, doi: <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","ama":"Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>. 2020;378(2):917-941. doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>"}},{"issue":"2","year":"2020","publisher":"Springer Science and Business Media LLC","date_created":"2024-04-11T12:33:03Z","title":"Pollicott-Ruelle Resonant States and Betti Numbers","publication":"Communications in Mathematical Physics","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n</jats:p>"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","intvolume":"       378","page":"917-941","citation":{"ama":"Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>. 2020;378(2):917-941. doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>","ieee":"B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, pp. 917–941, 2020, doi: <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>.","chicago":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i> 378, no. 2 (2020): 917–41. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>.","apa":"Küster, B., &#38; Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti Numbers. <i>Communications in Mathematical Physics</i>, <i>378</i>(2), 917–941. <a href=\"https://doi.org/10.1007/s00220-020-03793-2\">https://doi.org/10.1007/s00220-020-03793-2</a>","bibtex":"@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias}, year={2020}, pages={917–941} }","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","mla":"Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 2, Springer Science and Business Media LLC, 2020, pp. 917–41, doi:<a href=\"https://doi.org/10.1007/s00220-020-03793-2\">10.1007/s00220-020-03793-2</a>."},"date_updated":"2024-04-11T12:36:53Z","volume":378,"author":[{"full_name":"Küster, Benjamin","last_name":"Küster","first_name":"Benjamin"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias"}],"doi":"10.1007/s00220-020-03793-2","type":"journal_article","status":"public","_id":"53415","department":[{"_id":"548"}],"user_id":"70575"},{"doi":"10.1063/1.5140201","title":"Noether’s-type theorems on time scales","volume":61,"author":[{"first_name":"Baptiste","last_name":"Anerot","full_name":"Anerot, Baptiste"},{"last_name":"Cresson","full_name":"Cresson, Jacky","first_name":"Jacky"},{"full_name":"Hariz Belgacem, Khaled","last_name":"Hariz Belgacem","first_name":"Khaled"},{"first_name":"Frederic","full_name":"Pierret, Frederic","last_name":"Pierret"}],"date_created":"2023-01-24T10:29:55Z","date_updated":"2023-07-27T16:07:11Z","publisher":"AIP Publishing","intvolume":"        61","citation":{"chicago":"Anerot, Baptiste, Jacky Cresson, Khaled Hariz Belgacem, and Frederic Pierret. “Noether’s-Type Theorems on Time Scales.” <i>Journal of Mathematical Physics</i> 61, no. 11 (2020). <a href=\"https://doi.org/10.1063/1.5140201\">https://doi.org/10.1063/1.5140201</a>.","ieee":"B. Anerot, J. Cresson, K. Hariz Belgacem, and F. Pierret, “Noether’s-type theorems on time scales,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 11, Art. no. 113502, 2020, doi: <a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>.","ama":"Anerot B, Cresson J, Hariz Belgacem K, Pierret F. Noether’s-type theorems on time scales. <i>Journal of Mathematical Physics</i>. 2020;61(11). doi:<a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>","apa":"Anerot, B., Cresson, J., Hariz Belgacem, K., &#38; Pierret, F. (2020). Noether’s-type theorems on time scales. <i>Journal of Mathematical Physics</i>, <i>61</i>(11), Article 113502. <a href=\"https://doi.org/10.1063/1.5140201\">https://doi.org/10.1063/1.5140201</a>","mla":"Anerot, Baptiste, et al. “Noether’s-Type Theorems on Time Scales.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 11, 113502, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>.","bibtex":"@article{Anerot_Cresson_Hariz Belgacem_Pierret_2020, title={Noether’s-type theorems on time scales}, volume={61}, DOI={<a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>}, number={11113502}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Anerot, Baptiste and Cresson, Jacky and Hariz Belgacem, Khaled and Pierret, Frederic}, year={2020} }","short":"B. Anerot, J. Cresson, K. Hariz Belgacem, F. Pierret, Journal of Mathematical Physics 61 (2020)."},"year":"2020","issue":"11","publication_identifier":{"issn":["0022-2488","1089-7658"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_number":"113502","user_id":"98857","_id":"39414","status":"public","publication":"Journal of Mathematical Physics","type":"journal_article"},{"year":"2020","intvolume":"        61","citation":{"ama":"Anerot B, Cresson J, Hariz Belgacem K, Pierret F. Noether’s-type theorems on time scales. <i>Journal of Mathematical Physics</i>. 2020;61(11). doi:<a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>","chicago":"Anerot, Baptiste, Jacky Cresson, Khaled Hariz Belgacem, and Frederic Pierret. “Noether’s-Type Theorems on Time Scales.” <i>Journal of Mathematical Physics</i> 61, no. 11 (2020). <a href=\"https://doi.org/10.1063/1.5140201\">https://doi.org/10.1063/1.5140201</a>.","ieee":"B. Anerot, J. Cresson, K. Hariz Belgacem, and F. Pierret, “Noether’s-type theorems on time scales,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 11, Art. no. 113502, 2020, doi: <a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>.","apa":"Anerot, B., Cresson, J., Hariz Belgacem, K., &#38; Pierret, F. (2020). Noether’s-type theorems on time scales. <i>Journal of Mathematical Physics</i>, <i>61</i>(11), Article 113502. <a href=\"https://doi.org/10.1063/1.5140201\">https://doi.org/10.1063/1.5140201</a>","bibtex":"@article{Anerot_Cresson_Hariz Belgacem_Pierret_2020, title={Noether’s-type theorems on time scales}, volume={61}, DOI={<a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>}, number={11113502}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Anerot, Baptiste and Cresson, Jacky and Hariz Belgacem, Khaled and Pierret, Frederic}, year={2020} }","short":"B. Anerot, J. Cresson, K. Hariz Belgacem, F. Pierret, Journal of Mathematical Physics 61 (2020).","mla":"Anerot, Baptiste, et al. “Noether’s-Type Theorems on Time Scales.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 11, 113502, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/1.5140201\">10.1063/1.5140201</a>."},"publication_identifier":{"issn":["0022-2488","1089-7658"]},"publication_status":"published","issue":"11","title":"Noether’s-type theorems on time scales","doi":"10.1063/1.5140201","publisher":"AIP Publishing","date_updated":"2023-08-01T11:51:51Z","volume":61,"date_created":"2023-01-24T10:17:50Z","author":[{"full_name":"Anerot, Baptiste","last_name":"Anerot","first_name":"Baptiste"},{"full_name":"Cresson, Jacky","last_name":"Cresson","first_name":"Jacky"},{"first_name":"Khaled","id":"98857","full_name":"Hariz Belgacem, Khaled","last_name":"Hariz Belgacem"},{"first_name":"Frederic","full_name":"Pierret, Frederic","last_name":"Pierret"}],"status":"public","publication":"Journal of Mathematical Physics","type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_number":"113502","extern":"1","language":[{"iso":"eng"}],"_id":"39399","user_id":"98857"},{"external_id":{"arxiv":["1504.06728"]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","publisher":"Springer Science and Business Media LLC","date_created":"2022-05-17T12:11:13Z","title":"Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps","issue":"3","year":"2017","_id":"31268","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"journal_article","status":"public","date_updated":"2022-05-19T10:14:36Z","author":[{"first_name":"Frédéric","full_name":"Faure, Frédéric","last_name":"Faure"},{"first_name":"Tobias","full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"volume":356,"doi":"10.1007/s00220-017-3000-0","publication_status":"published","publication_identifier":{"issn":["0010-3616","1432-0916"]},"citation":{"chicago":"Faure, Frédéric, and Tobias Weich. “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps.” <i>Communications in Mathematical Physics</i> 356, no. 3 (2017): 755–822. <a href=\"https://doi.org/10.1007/s00220-017-3000-0\">https://doi.org/10.1007/s00220-017-3000-0</a>.","ieee":"F. Faure and T. Weich, “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps,” <i>Communications in Mathematical Physics</i>, vol. 356, no. 3, pp. 755–822, 2017, doi: <a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>.","ama":"Faure F, Weich T. Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. <i>Communications in Mathematical Physics</i>. 2017;356(3):755-822. doi:<a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>","bibtex":"@article{Faure_Weich_2017, title={Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps}, volume={356}, DOI={<a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Faure, Frédéric and Weich, Tobias}, year={2017}, pages={755–822} }","mla":"Faure, Frédéric, and Tobias Weich. “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps.” <i>Communications in Mathematical Physics</i>, vol. 356, no. 3, Springer Science and Business Media LLC, 2017, pp. 755–822, doi:<a href=\"https://doi.org/10.1007/s00220-017-3000-0\">10.1007/s00220-017-3000-0</a>.","short":"F. Faure, T. Weich, Communications in Mathematical Physics 356 (2017) 755–822.","apa":"Faure, F., &#38; Weich, T. (2017). 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