[{"publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","citation":{"ama":"Winkler M. A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>. Published online 2023. doi:<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>","bibtex":"@article{Winkler_2023, title={A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion}, DOI={<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2023} }","mla":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, European Mathematical Society - EMS - Publishing House GmbH, 2023, doi:<a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>.","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire (2023).","chicago":"Winkler, Michael. “A Quantitative Strong Parabolic Maximum Principle and Application to a Taxis-Type Migration–Consumption Model Involving Signal-Dependent Degenerate Diffusion.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, 2023. <a href=\"https://doi.org/10.4171/aihpc/73\">https://doi.org/10.4171/aihpc/73</a>.","apa":"Winkler, M. (2023). A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion. <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>. <a href=\"https://doi.org/10.4171/aihpc/73\">https://doi.org/10.4171/aihpc/73</a>","ieee":"M. Winkler, “A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion,” <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>, 2023, doi: <a href=\"https://doi.org/10.4171/aihpc/73\">10.4171/aihpc/73</a>."},"date_created":"2024-04-07T12:34:35Z","type":"journal_article","keyword":["Mathematical Physics","Analysis","Applied Mathematics"],"year":"2023","status":"public","title":"A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion","author":[{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["0294-1449","1873-1430"]},"publication_status":"published","date_updated":"2024-04-07T12:36:00Z","_id":"53320","language":[{"iso":"eng"}],"publisher":"European Mathematical Society - EMS - Publishing House GmbH","user_id":"31496","doi":"10.4171/aihpc/73"},{"date_created":"2024-04-07T12:56:35Z","keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","publication":"Nonlinearity","issue":"8","abstract":[{"lang":"eng","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>"}],"language":[{"iso":"eng"}],"doi":"10.1088/1361-6544/ace22e","title":"Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction","year":"2023","author":[{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"date_updated":"2024-04-07T12:56:40Z","publication_status":"published","intvolume":"        36","citation":{"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>","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} }","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>.","short":"M. Winkler, Nonlinearity 36 (2023) 4438–4469.","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>.","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>","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>."},"page":"4438-4469","_id":"53345","publisher":"IOP Publishing","user_id":"31496","volume":36,"status":"public"},{"doi":"10.1007/s00023-023-01379-x","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2024-04-11T12:37:34Z","intvolume":"        25","year":"2023","title":"Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models","author":[{"id":"70575","full_name":"Delarue, Benjamin","first_name":"Benjamin","last_name":"Delarue"},{"full_name":"Schütte, Philipp","first_name":"Philipp","last_name":"Schütte","id":"50168"},{"id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias","full_name":"Weich, Tobias"}],"publication_identifier":{"issn":["1424-0637","1424-0661"]},"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"type":"journal_article","department":[{"_id":"548"}],"date_created":"2024-04-11T12:30:14Z","abstract":[{"lang":"eng","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>"}],"publication":"Annales Henri Poincaré","issue":"2","user_id":"70575","volume":25,"page":"1607-1656","publisher":"Springer Science and Business Media LLC","_id":"53410","status":"public","citation":{"short":"B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.","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>.","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>","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} }","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>","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>."}},{"citation":{"chicago":"Serino, Laura, Jano Gil López, Michael Stefszky, Raimund Ricken, Christof Eigner, Benjamin Brecht, and Christine Silberhorn. “Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States.” <i>PRX Quantum</i> 4, no. 2 (2023). <a href=\"https://doi.org/10.1103/prxquantum.4.020306\">https://doi.org/10.1103/prxquantum.4.020306</a>.","short":"L. Serino, J. Gil López, M. Stefszky, R. Ricken, C. Eigner, B. Brecht, C. Silberhorn, PRX Quantum 4 (2023).","apa":"Serino, L., Gil López, J., Stefszky, M., Ricken, R., Eigner, C., Brecht, B., &#38; Silberhorn, C. (2023). Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States. <i>PRX Quantum</i>, <i>4</i>(2), Article 020306. <a href=\"https://doi.org/10.1103/prxquantum.4.020306\">https://doi.org/10.1103/prxquantum.4.020306</a>","ieee":"L. Serino <i>et al.</i>, “Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States,” <i>PRX Quantum</i>, vol. 4, no. 2, Art. no. 020306, 2023, doi: <a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>.","ama":"Serino L, Gil López J, Stefszky M, et al. Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States. <i>PRX Quantum</i>. 2023;4(2). doi:<a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>","bibtex":"@article{Serino_Gil López_Stefszky_Ricken_Eigner_Brecht_Silberhorn_2023, title={Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States}, volume={4}, DOI={<a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>}, number={2020306}, journal={PRX Quantum}, publisher={American Physical Society (APS)}, author={Serino, Laura and Gil López, Jano and Stefszky, Michael and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}, year={2023} }","mla":"Serino, Laura, et al. “Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States.” <i>PRX Quantum</i>, vol. 4, no. 2, 020306, American Physical Society (APS), 2023, doi:<a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>."},"status":"public","user_id":"27150","volume":4,"_id":"44081","publisher":"American Physical Society (APS)","publication":"PRX Quantum","issue":"2","type":"journal_article","keyword":["General Physics and Astronomy","Mathematical Physics","Applied Mathematics","Electronic","Optical and Magnetic Materials","Electrical and Electronic Engineering","General Computer Science"],"department":[{"_id":"288"},{"_id":"623"},{"_id":"15"}],"date_created":"2023-04-20T12:38:23Z","publication_status":"published","date_updated":"2025-12-18T16:15:18Z","intvolume":"         4","title":"Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States","year":"2023","publication_identifier":{"issn":["2691-3399"]},"author":[{"id":"88242","full_name":"Serino, Laura","last_name":"Serino","first_name":"Laura"},{"id":"51223","full_name":"Gil López, Jano","last_name":"Gil López","first_name":"Jano"},{"last_name":"Stefszky","first_name":"Michael","full_name":"Stefszky, Michael","id":"42777"},{"full_name":"Ricken, Raimund","last_name":"Ricken","first_name":"Raimund"},{"id":"13244","full_name":"Eigner, Christof","first_name":"Christof","last_name":"Eigner","orcid":"https://orcid.org/0000-0002-5693-3083"},{"id":"27150","orcid":"0000-0003-4140-0556 ","last_name":"Brecht","first_name":"Benjamin","full_name":"Brecht, Benjamin"},{"id":"26263","full_name":"Silberhorn, Christine","last_name":"Silberhorn","first_name":"Christine"}],"doi":"10.1103/prxquantum.4.020306","article_number":"020306","language":[{"iso":"eng"}]},{"keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","date_created":"2022-09-06T11:38:15Z","extern":"1","abstract":[{"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.","lang":"eng"}],"publication":"Nonlinearity","issue":"4","doi":"10.1088/1361-6544/ac5463","language":[{"iso":"eng"}],"intvolume":"        35","publication_status":"published","date_updated":"2022-09-07T08:36:46Z","author":[{"last_name":"von der Gracht","first_name":"Sören","orcid":"0000-0002-8054-2058","full_name":"von der Gracht, Sören","id":"97359"},{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"last_name":"Rink","first_name":"Bob","full_name":"Rink, Bob"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"title":"Amplified steady state bifurcations in feedforward networks","year":"2022","external_id":{"arxiv":["2105.02547"]},"citation":{"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>.","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} }","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>","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>.","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>","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>.","short":"S. von der Gracht, E. Nijholt, B. Rink, Nonlinearity 35 (2022) 2073–2120."},"volume":35,"user_id":"97359","_id":"33264","publisher":"IOP Publishing","page":"2073-2120","status":"public"},{"article_number":"2200049","_id":"33332","language":[{"iso":"eng"}],"publisher":"Wiley","doi":"10.1002/qute.202200049","user_id":"42514","year":"2022","title":"Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling","status":"public","publication_identifier":{"issn":["2511-9044","2511-9044"]},"author":[{"full_name":"Bopp, Frederik","first_name":"Frederik","last_name":"Bopp"},{"first_name":"Jonathan","last_name":"Rojas","full_name":"Rojas, Jonathan"},{"full_name":"Revenga, Natalia","last_name":"Revenga","first_name":"Natalia"},{"full_name":"Riedl, Hubert","last_name":"Riedl","first_name":"Hubert"},{"last_name":"Sbresny","first_name":"Friedrich","full_name":"Sbresny, Friedrich"},{"last_name":"Boos","first_name":"Katarina","full_name":"Boos, Katarina"},{"full_name":"Simmet, Tobias","last_name":"Simmet","first_name":"Tobias"},{"last_name":"Ahmadi","first_name":"Arash","full_name":"Ahmadi, Arash"},{"last_name":"Gershoni","first_name":"David","full_name":"Gershoni, David"},{"last_name":"Kasprzak","first_name":"Jacek","full_name":"Kasprzak, Jacek"},{"full_name":"Ludwig, Arne","last_name":"Ludwig","first_name":"Arne"},{"full_name":"Reitzenstein, Stephan","first_name":"Stephan","last_name":"Reitzenstein"},{"first_name":"Andreas","last_name":"Wieck","full_name":"Wieck, Andreas"},{"first_name":"Dirk","last_name":"Reuter","full_name":"Reuter, Dirk","id":"37763"},{"last_name":"Müller","first_name":"Kai","full_name":"Müller, Kai"},{"first_name":"Jonathan J.","last_name":"Finley","full_name":"Finley, Jonathan J."}],"date_updated":"2022-09-12T07:18:06Z","publication_status":"published","date_created":"2022-09-12T07:17:26Z","type":"journal_article","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"],"department":[{"_id":"15"},{"_id":"230"}],"publication":"Advanced Quantum Technologies","citation":{"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} }","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).","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>","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>.","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>.","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>"}},{"doi":"10.4171/jst/414","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2024-02-19T06:28:12Z","intvolume":"        12","year":"2022","title":"Poisson transforms for trees of bounded degree","publication_identifier":{"issn":["1664-039X"]},"author":[{"last_name":"Bux","first_name":"Kai-Uwe","full_name":"Bux, Kai-Uwe"},{"id":"220","full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","first_name":"Tobias","orcid":"0000-0002-9648-6919"}],"keyword":["Geometry and Topology","Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"date_created":"2023-01-06T08:49:06Z","issue":"2","publication":"Journal of Spectral Theory","user_id":"49063","volume":12,"page":"659-681","_id":"35322","publisher":"European Mathematical Society - EMS - Publishing House GmbH","status":"public","citation":{"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>.","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>","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} }","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>","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>.","short":"K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.","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>."}},{"publication":"Annales Henri Poincaré","issue":"11","department":[{"_id":"548"}],"type":"journal_article","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"date_created":"2022-06-20T08:37:52Z","intvolume":"        22","date_updated":"2024-04-11T12:39:23Z","publication_status":"published","author":[{"last_name":"Guillarmou","first_name":"Colin","full_name":"Guillarmou, Colin"},{"full_name":"Küster, Benjamin","first_name":"Benjamin","last_name":"Küster"}],"publication_identifier":{"issn":["1424-0637","1424-0661"]},"title":"Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds","year":"2021","doi":"10.1007/s00023-021-01068-7","language":[{"iso":"eng"}],"citation":{"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>.","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>","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} }","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>","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>.","short":"C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617."},"status":"public","volume":22,"user_id":"70575","publisher":"Springer Science and Business Media LLC","_id":"32006","page":"3565-3617"},{"department":[{"_id":"15"},{"_id":"230"}],"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"],"type":"journal_article","date_created":"2023-07-25T08:45:57Z","issue":"6","publication":"Advanced Quantum Technologies","doi":"10.1002/qute.202100002","language":[{"iso":"eng"}],"article_number":"2100002","intvolume":"         4","date_updated":"2023-07-25T08:46:47Z","publication_status":"published","author":[{"full_name":"Schall, Johannes","last_name":"Schall","first_name":"Johannes"},{"last_name":"Deconinck","first_name":"Marielle","full_name":"Deconinck, Marielle"},{"last_name":"Bart","first_name":"Nikolai","full_name":"Bart, Nikolai"},{"first_name":"Matthias","last_name":"Florian","full_name":"Florian, Matthias"},{"first_name":"Martin","last_name":"Helversen","full_name":"Helversen, Martin"},{"first_name":"Christian","last_name":"Dangel","full_name":"Dangel, Christian"},{"full_name":"Schmidt, Ronny","last_name":"Schmidt","first_name":"Ronny"},{"full_name":"Bremer, Lucas","first_name":"Lucas","last_name":"Bremer"},{"last_name":"Bopp","first_name":"Frederik","full_name":"Bopp, Frederik"},{"full_name":"Hüllen, Isabell","first_name":"Isabell","last_name":"Hüllen"},{"full_name":"Gies, Christopher","last_name":"Gies","first_name":"Christopher"},{"id":"37763","full_name":"Reuter, Dirk","first_name":"Dirk","last_name":"Reuter"},{"last_name":"Wieck","first_name":"Andreas D.","full_name":"Wieck, Andreas D."},{"last_name":"Rodt","first_name":"Sven","full_name":"Rodt, Sven"},{"full_name":"Finley, Jonathan J.","last_name":"Finley","first_name":"Jonathan J."},{"first_name":"Frank","last_name":"Jahnke","full_name":"Jahnke, Frank"},{"full_name":"Ludwig, Arne","last_name":"Ludwig","first_name":"Arne"},{"last_name":"Reitzenstein","first_name":"Stephan","full_name":"Reitzenstein, Stephan"}],"publication_identifier":{"issn":["2511-9044","2511-9044"]},"title":"Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography","year":"2021","citation":{"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>.","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>","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).","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>.","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>.","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} }","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>"},"volume":4,"user_id":"42514","_id":"46135","publisher":"Wiley","status":"public"},{"language":[{"iso":"eng"}],"doi":"10.1007/s00220-020-03793-2","publication_identifier":{"issn":["0010-3616","1432-0916"]},"author":[{"last_name":"Küster","first_name":"Benjamin","full_name":"Küster, Benjamin"},{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178"}],"title":"Pollicott-Ruelle Resonant States and Betti Numbers","year":"2020","intvolume":"       378","publication_status":"published","date_updated":"2022-05-19T10:13:48Z","date_created":"2022-05-17T12:06:06Z","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publication":"Communications in Mathematical Physics","issue":"2","abstract":[{"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>","lang":"eng"}],"publisher":"Springer Science and Business Media LLC","_id":"31264","page":"917-941","volume":378,"user_id":"49178","status":"public","citation":{"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>.","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>","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","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>.","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} }","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>"}},{"citation":{"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>.","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>","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","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>.","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} }","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>"},"status":"public","user_id":"70575","volume":378,"page":"917-941","_id":"53415","publisher":"Springer Science and Business Media LLC","abstract":[{"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>","lang":"eng"}],"issue":"2","publication":"Communications in Mathematical Physics","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","department":[{"_id":"548"}],"date_created":"2024-04-11T12:33:03Z","date_updated":"2024-04-11T12:36:53Z","publication_status":"published","intvolume":"       378","year":"2020","title":"Pollicott-Ruelle Resonant States and Betti Numbers","author":[{"full_name":"Küster, Benjamin","first_name":"Benjamin","last_name":"Küster"},{"last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias","full_name":"Weich, Tobias","id":"49178"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"doi":"10.1007/s00220-020-03793-2","language":[{"iso":"eng"}]},{"article_number":"113502","language":[{"iso":"eng"}],"doi":"10.1063/1.5140201","year":"2020","title":"Noether’s-type theorems on time scales","publication_identifier":{"issn":["0022-2488","1089-7658"]},"author":[{"first_name":"Baptiste","last_name":"Anerot","full_name":"Anerot, Baptiste"},{"full_name":"Cresson, Jacky","last_name":"Cresson","first_name":"Jacky"},{"full_name":"Hariz Belgacem, Khaled","first_name":"Khaled","last_name":"Hariz Belgacem"},{"first_name":"Frederic","last_name":"Pierret","full_name":"Pierret, Frederic"}],"publication_status":"published","date_updated":"2023-07-27T16:07:11Z","intvolume":"        61","date_created":"2023-01-24T10:29:55Z","type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publication":"Journal of Mathematical Physics","issue":"11","publisher":"AIP Publishing","_id":"39414","user_id":"98857","volume":61,"status":"public","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>","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} }","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>.","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>.","short":"B. Anerot, J. Cresson, K. Hariz Belgacem, F. Pierret, Journal of Mathematical Physics 61 (2020).","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>","ieee":"B. Anerot, J. Cresson, K. Hariz Belgacem, and F. 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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>"},"user_id":"98857","volume":61,"publisher":"AIP Publishing","_id":"39399","status":"public","type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2023-01-24T10:17:50Z","extern":"1","publication":"Journal of Mathematical Physics","issue":"11","doi":"10.1063/1.5140201","article_number":"113502","language":[{"iso":"eng"}],"date_updated":"2023-08-01T11:51:51Z","publication_status":"published","intvolume":"        61","year":"2020","title":"Noether’s-type theorems on time scales","author":[{"last_name":"Anerot","first_name":"Baptiste","full_name":"Anerot, Baptiste"},{"last_name":"Cresson","first_name":"Jacky","full_name":"Cresson, Jacky"},{"id":"98857","full_name":"Hariz Belgacem, Khaled","last_name":"Hariz Belgacem","first_name":"Khaled"},{"full_name":"Pierret, Frederic","last_name":"Pierret","first_name":"Frederic"}],"publication_identifier":{"issn":["0022-2488","1089-7658"]}},{"date_updated":"2022-12-21T10:04:29Z","publication_status":"published","intvolume":"        22","year":"2019","title":"The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System","author":[{"orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black","full_name":"Black, Tobias","id":"23686"}],"publication_identifier":{"issn":["1422-6928","1422-6952"]},"doi":"10.1007/s00021-019-0464-z","article_number":"1","language":[{"iso":"eng"}],"publication":"Journal of Mathematical Fluid Mechanics","issue":"1","keyword":["Applied Mathematics","Computational Mathematics","Condensed Matter Physics","Mathematical Physics"],"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2022-12-21T09:47:56Z","status":"public","user_id":"23686","volume":22,"_id":"34669","publisher":"Springer Science and Business Media LLC","citation":{"mla":"Black, Tobias. “The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 22, no. 1, 1, Springer Science and Business Media LLC, 2019, doi:<a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>.","apa":"Black, T. (2019). The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System. <i>Journal of Mathematical Fluid Mechanics</i>, <i>22</i>(1), Article 1. <a href=\"https://doi.org/10.1007/s00021-019-0464-z\">https://doi.org/10.1007/s00021-019-0464-z</a>","ieee":"T. Black, “The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System,” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 22, no. 1, Art. no. 1, 2019, doi: <a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>.","short":"T. Black, Journal of Mathematical Fluid Mechanics 22 (2019).","ama":"Black T. The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System. <i>Journal of Mathematical Fluid Mechanics</i>. 2019;22(1). doi:<a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>","chicago":"Black, Tobias. “The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Mathematical Fluid Mechanics</i> 22, no. 1 (2019). <a href=\"https://doi.org/10.1007/s00021-019-0464-z\">https://doi.org/10.1007/s00021-019-0464-z</a>.","bibtex":"@article{Black_2019, title={The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System}, volume={22}, DOI={<a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>}, number={11}, journal={Journal of Mathematical Fluid Mechanics}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias}, year={2019} }"}},{"status":"public","publisher":"Springer Science and Business Media LLC","_id":"31268","page":"755-822","volume":356,"user_id":"49178","citation":{"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>.","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} }","ama":"Faure F, Weich T. 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