[{"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"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"}],"publication":"Communications in Mathematical Physics","title":"Pollicott-Ruelle Resonant States and Betti Numbers","publisher":"Springer Science and Business Media LLC","date_created":"2022-05-17T12:06:06Z","year":"2020","issue":"2","_id":"31264","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","status":"public","type":"journal_article","doi":"10.1007/s00220-020-03793-2","date_updated":"2022-05-19T10:13:48Z","volume":378,"author":[{"first_name":"Benjamin","full_name":"Küster, Benjamin","last_name":"Küster"},{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias"}],"page":"917-941","intvolume":"       378","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>","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>.","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>","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>.","short":"B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941.","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} }"},"publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published"},{"doi":"10.1007/s00220-020-03793-2","date_updated":"2024-04-11T12:36:53Z","author":[{"last_name":"Küster","full_name":"Küster, Benjamin","first_name":"Benjamin"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"}],"volume":378,"citation":{"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>","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.","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>","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>."},"intvolume":"       378","page":"917-941","publication_status":"published","publication_identifier":{"issn":["0010-3616","1432-0916"]},"_id":"53415","user_id":"70575","department":[{"_id":"548"}],"status":"public","type":"journal_article","title":"Pollicott-Ruelle Resonant States and Betti Numbers","publisher":"Springer Science and Business Media LLC","date_created":"2024-04-11T12:33:03Z","year":"2020","issue":"2","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"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>"}],"publication":"Communications in Mathematical Physics"},{"intvolume":"        21","page":"1595-1639","citation":{"apa":"Dyatlov, S., Borthwick, D., &#38; Weich, T. (2019). Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich. <i>Journal of the European Mathematical Society</i>, <i>21</i>(6), 1595–1639. <a href=\"https://doi.org/10.4171/jems/867\">https://doi.org/10.4171/jems/867</a>","short":"S. Dyatlov, D. Borthwick, T. Weich, Journal of the European Mathematical Society 21 (2019) 1595–1639.","bibtex":"@article{Dyatlov_Borthwick_Weich_2019, title={Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich}, volume={21}, DOI={<a href=\"https://doi.org/10.4171/jems/867\">10.4171/jems/867</a>}, number={6}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Dyatlov, Semyon and Borthwick, David and Weich, Tobias}, year={2019}, pages={1595–1639} }","mla":"Dyatlov, Semyon, et al. “Improved Fractal Weyl Bounds for Hyperbolic Manifolds. With an Appendix by David Borthwick, Semyon Dyatlov and Tobias Weich.” <i>Journal of the European Mathematical Society</i>, vol. 21, no. 6, European Mathematical Society - EMS - Publishing House GmbH, 2019, pp. 1595–639, doi:<a href=\"https://doi.org/10.4171/jems/867\">10.4171/jems/867</a>.","chicago":"Dyatlov, Semyon, David Borthwick, and Tobias Weich. “Improved Fractal Weyl Bounds for Hyperbolic Manifolds. With an Appendix by David Borthwick, Semyon Dyatlov and Tobias Weich.” <i>Journal of the European Mathematical Society</i> 21, no. 6 (2019): 1595–1639. <a href=\"https://doi.org/10.4171/jems/867\">https://doi.org/10.4171/jems/867</a>.","ieee":"S. Dyatlov, D. Borthwick, and T. Weich, “Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich,” <i>Journal of the European Mathematical Society</i>, vol. 21, no. 6, pp. 1595–1639, 2019, doi: <a href=\"https://doi.org/10.4171/jems/867\">10.4171/jems/867</a>.","ama":"Dyatlov S, Borthwick D, Weich T. Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich. <i>Journal of the European Mathematical Society</i>. 2019;21(6):1595-1639. doi:<a href=\"https://doi.org/10.4171/jems/867\">10.4171/jems/867</a>"},"publication_identifier":{"issn":["1435-9855"]},"publication_status":"published","doi":"10.4171/jems/867","date_updated":"2022-05-19T10:12:59Z","volume":21,"author":[{"last_name":"Dyatlov","full_name":"Dyatlov, Semyon","first_name":"Semyon"},{"full_name":"Borthwick, David","last_name":"Borthwick","first_name":"David"},{"full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"}],"status":"public","type":"journal_article","_id":"31265","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","year":"2019","issue":"6","title":"Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich","publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_created":"2022-05-17T12:06:41Z","publication":"Journal of the European Mathematical Society","keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1512.00836"]}},{"external_id":{"arxiv":["1909.06183"]},"_id":"31191","user_id":"45027","department":[{"_id":"548"}],"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:1909.06183","abstract":[{"text":"The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$\r\nis a stochastic process that models a random perturbation of the geodesic flow.\r\nIf $M$ is a orientable compact constant negatively curved surface, we show that\r\nin the limit of infinitely large perturbation the $L^2$-spectrum of the\r\ninfinitesimal generator of a time rescaled version of the process converges to\r\nthe Laplace spectrum of the base manifold. In addition, we give explicit error\r\nestimates for the convergence to equilibrium. The proofs are based on\r\nnoncommutative harmonic analysis of $SL_2(\\mathbb{R})$.","lang":"eng"}],"status":"public","date_updated":"2022-05-24T13:06:58Z","author":[{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178"},{"first_name":"Lasse Lennart","id":"45027","full_name":"Wolf, Lasse Lennart","last_name":"Wolf"}],"date_created":"2022-05-11T10:42:11Z","title":"Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces","year":"2019","citation":{"ama":"Kolb M, Weich T, Wolf LL. Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. <i>arXiv:190906183</i>. Published online 2019.","ieee":"M. Kolb, T. Weich, and L. L. Wolf, “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces,” <i>arXiv:1909.06183</i>. 2019.","chicago":"Kolb, Martin, Tobias Weich, and Lasse Lennart Wolf. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces.” <i>ArXiv:1909.06183</i>, 2019.","short":"M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (2019).","mla":"Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces.” <i>ArXiv:1909.06183</i>, 2019.","bibtex":"@article{Kolb_Weich_Wolf_2019, title={Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces}, journal={arXiv:1909.06183}, author={Kolb, Martin and Weich, Tobias and Wolf, Lasse Lennart}, year={2019} }","apa":"Kolb, M., Weich, T., &#38; Wolf, L. L. (2019). Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. In <i>arXiv:1909.06183</i>."}},{"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"53416","user_id":"70575","department":[{"_id":"548"}],"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>For a compact Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$ over $\\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau }$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>"}],"status":"public","type":"journal_article","publication":"International Mathematics Research Notices","title":"Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces","doi":"10.1093/imrn/rnz068","publisher":"Oxford University Press (OUP)","date_updated":"2024-04-11T12:36:33Z","date_created":"2024-04-11T12:33:46Z","author":[{"last_name":"Küster","full_name":"Küster, Benjamin","first_name":"Benjamin"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich"}],"volume":2021,"year":"2019","citation":{"ama":"Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>. 2019;2021(11):8225-8296. doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>","chicago":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i> 2021, no. 11 (2019): 8225–96. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>.","ieee":"B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces,” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, pp. 8225–8296, 2019, doi: <a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>.","apa":"Küster, B., &#38; Weich, T. (2019). Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>, <i>2021</i>(11), 8225–8296. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>","mla":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2019, pp. 8225–96, doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>.","short":"B. Küster, T. Weich, International Mathematics Research Notices 2021 (2019) 8225–8296.","bibtex":"@article{Küster_Weich_2019, title={Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>}, number={11}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2019}, pages={8225–8296} }"},"page":"8225-8296","intvolume":"      2021","publication_status":"published","publication_identifier":{"issn":["1073-7928","1687-0247"]},"issue":"11"},{"status":"public","type":"journal_article","publication":"Math. Ann.","language":[{"iso":"eng"}],"_id":"51389","user_id":"220","department":[{"_id":"91"}],"year":"2018","citation":{"ieee":"J. Hilgert, T. Weich, and C. Guillarmou, “Classical and quantum resonances for hyperbolic surfaces,” <i>Math. Ann.</i>, vol. 370, pp. 1231–1275, 2018.","chicago":"Hilgert, Joachim, Tobias Weich, and C. Guillarmou. “Classical and Quantum Resonances for Hyperbolic Surfaces.” <i>Math. Ann.</i> 370 (2018): 1231–75.","ama":"Hilgert J, Weich T, Guillarmou C. Classical and quantum resonances for hyperbolic surfaces. <i>Math Ann</i>. 2018;370:1231-1275.","apa":"Hilgert, J., Weich, T., &#38; Guillarmou, C. (2018). Classical and quantum resonances for hyperbolic surfaces. <i>Math. Ann.</i>, <i>370</i>, 1231–1275.","mla":"Hilgert, Joachim, et al. “Classical and Quantum Resonances for Hyperbolic Surfaces.” <i>Math. Ann.</i>, vol. 370, 2018, pp. 1231–75.","bibtex":"@article{Hilgert_Weich_Guillarmou_2018, title={Classical and quantum resonances for hyperbolic surfaces}, volume={370}, journal={Math. Ann.}, author={Hilgert, Joachim and Weich, Tobias and Guillarmou, C.}, year={2018}, pages={1231–1275} }","short":"J. Hilgert, T. Weich, C. Guillarmou, Math. Ann. 370 (2018) 1231–1275."},"intvolume":"       370","page":"1231-1275","publication_status":"published","title":"Classical and quantum resonances for hyperbolic surfaces","date_updated":"2026-03-31T08:24:58Z","date_created":"2024-02-19T06:41:17Z","author":[{"full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert","first_name":"Joachim"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"first_name":"C.","full_name":"Guillarmou, C.","last_name":"Guillarmou"}],"volume":370},{"doi":"10.1007/s00220-017-3000-0","volume":356,"author":[{"first_name":"Frédéric","full_name":"Faure, Frédéric","last_name":"Faure"},{"last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"}],"date_updated":"2022-05-19T10:14:36Z","page":"755-822","intvolume":"       356","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} }","short":"F. Faure, T. Weich, Communications in Mathematical Physics 356 (2017) 755–822.","apa":"Faure, F., &#38; Weich, T. (2017). Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. <i>Communications in Mathematical Physics</i>, <i>356</i>(3), 755–822. <a href=\"https://doi.org/10.1007/s00220-017-3000-0\">https://doi.org/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>","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>.","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>."},"publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","_id":"31268","status":"public","type":"journal_article","title":"Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps","date_created":"2022-05-17T12:11:13Z","publisher":"Springer Science and Business Media LLC","year":"2017","issue":"3","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"external_id":{"arxiv":["1504.06728"]},"publication":"Communications in Mathematical Physics"},{"doi":"10.1016/j.aim.2017.03.025","volume":313,"author":[{"first_name":"Benjamin","full_name":"Harris, Benjamin","last_name":"Harris"},{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178"}],"date_updated":"2022-05-19T10:15:00Z","page":"176-236","intvolume":"       313","citation":{"apa":"Harris, B., &#38; Weich, T. (2017). Wave front sets of reductive Lie group representations III. <i>Advances in Mathematics</i>, <i>313</i>, 176–236. <a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">https://doi.org/10.1016/j.aim.2017.03.025</a>","mla":"Harris, Benjamin, and Tobias Weich. “Wave Front Sets of Reductive Lie Group Representations III.” <i>Advances in Mathematics</i>, vol. 313, Elsevier BV, 2017, pp. 176–236, doi:<a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>.","bibtex":"@article{Harris_Weich_2017, title={Wave front sets of reductive Lie group representations III}, volume={313}, DOI={<a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>}, journal={Advances in Mathematics}, publisher={Elsevier BV}, author={Harris, Benjamin and Weich, Tobias}, year={2017}, pages={176–236} }","short":"B. Harris, T. Weich, Advances in Mathematics 313 (2017) 176–236.","ieee":"B. Harris and T. Weich, “Wave front sets of reductive Lie group representations III,” <i>Advances in Mathematics</i>, vol. 313, pp. 176–236, 2017, doi: <a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>.","chicago":"Harris, Benjamin, and Tobias Weich. “Wave Front Sets of Reductive Lie Group Representations III.” <i>Advances in Mathematics</i> 313 (2017): 176–236. <a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">https://doi.org/10.1016/j.aim.2017.03.025</a>.","ama":"Harris B, Weich T. Wave front sets of reductive Lie group representations III. <i>Advances in Mathematics</i>. 2017;313:176-236. doi:<a href=\"https://doi.org/10.1016/j.aim.2017.03.025\">10.1016/j.aim.2017.03.025</a>"},"publication_identifier":{"issn":["0001-8708"]},"publication_status":"published","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","_id":"31272","status":"public","type":"journal_article","title":"Wave front sets of reductive Lie group representations III","date_created":"2022-05-17T12:16:37Z","publisher":"Elsevier BV","year":"2017","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"external_id":{"arxiv":["1503.08431"]},"publication":"Advances in Mathematics"},{"year":"2017","issue":"3-4","title":"Classical and quantum resonances for hyperbolic surfaces","publisher":"Springer Science and Business Media LLC","date_created":"2022-05-17T12:09:43Z","publication":"Mathematische Annalen","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1605.08801"]},"citation":{"apa":"Guillarmou, C., Hilgert, J., &#38; Weich, T. (2017). Classical and quantum resonances for hyperbolic surfaces. <i>Mathematische Annalen</i>, <i>370</i>(3–4), 1231–1275. <a href=\"https://doi.org/10.1007/s00208-017-1576-5\">https://doi.org/10.1007/s00208-017-1576-5</a>","mla":"Guillarmou, Colin, et al. “Classical and Quantum Resonances for Hyperbolic Surfaces.” <i>Mathematische Annalen</i>, vol. 370, no. 3–4, Springer Science and Business Media LLC, 2017, pp. 1231–75, doi:<a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>.","short":"C. Guillarmou, J. Hilgert, T. Weich, Mathematische Annalen 370 (2017) 1231–1275.","bibtex":"@article{Guillarmou_Hilgert_Weich_2017, title={Classical and quantum resonances for hyperbolic surfaces}, volume={370}, DOI={<a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>}, number={3–4}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}, year={2017}, pages={1231–1275} }","ama":"Guillarmou C, Hilgert J, Weich T. Classical and quantum resonances for hyperbolic surfaces. <i>Mathematische Annalen</i>. 2017;370(3-4):1231-1275. doi:<a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>","chicago":"Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “Classical and Quantum Resonances for Hyperbolic Surfaces.” <i>Mathematische Annalen</i> 370, no. 3–4 (2017): 1231–75. <a href=\"https://doi.org/10.1007/s00208-017-1576-5\">https://doi.org/10.1007/s00208-017-1576-5</a>.","ieee":"C. Guillarmou, J. Hilgert, and T. Weich, “Classical and quantum resonances for hyperbolic surfaces,” <i>Mathematische Annalen</i>, vol. 370, no. 3–4, pp. 1231–1275, 2017, doi: <a href=\"https://doi.org/10.1007/s00208-017-1576-5\">10.1007/s00208-017-1576-5</a>."},"intvolume":"       370","page":"1231-1275","publication_status":"published","publication_identifier":{"issn":["0025-5831","1432-1807"]},"doi":"10.1007/s00208-017-1576-5","date_updated":"2024-02-19T06:18:21Z","author":[{"first_name":"Colin","full_name":"Guillarmou, Colin","last_name":"Guillarmou"},{"first_name":"Joachim","last_name":"Hilgert","id":"220","full_name":"Hilgert, Joachim"},{"first_name":"Tobias","full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich"}],"volume":370,"status":"public","type":"journal_article","_id":"31267","user_id":"49063","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}]},{"date_updated":"2023-07-19T13:59:03Z","oa":"1","date_created":"2022-05-22T15:00:35Z","author":[{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias"},{"first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max","id":"32202"}],"volume":3,"title":"Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.","main_file_link":[{"url":"http://www.hochschullehre.org/wp-content/files/diehochschullehre_2017_weich_hoffmann.pdf","open_access":"1"}],"publication_status":"published","quality_controlled":"1","year":"2017","citation":{"apa":"Weich, T., &#38; Hoffmann, M. (2017). Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt. <i>die hochschullehre</i>, <i>3</i>.","bibtex":"@article{Weich_Hoffmann_2017, title={Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.}, volume={3}, journal={die hochschullehre}, author={Weich, Tobias and Hoffmann, Max}, year={2017} }","short":"T. Weich, M. Hoffmann, die hochschullehre 3 (2017).","mla":"Weich, Tobias, and Max Hoffmann. “Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.” <i>die hochschullehre</i>, vol. 3, 2017.","chicago":"Weich, Tobias, and Max Hoffmann. “Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.” <i>die hochschullehre</i> 3 (2017).","ieee":"T. Weich and M. Hoffmann, “Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.,” <i>die hochschullehre</i>, vol. 3, 2017.","ama":"Weich T, Hoffmann M. Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt. <i>die hochschullehre</i>. 2017;3."},"intvolume":"         3","_id":"31377","user_id":"32202","department":[{"_id":"97"}],"article_type":"original","language":[{"iso":"ger"}],"type":"journal_article","publication":"die hochschullehre","status":"public"},{"date_updated":"2022-05-19T10:15:17Z","volume":6,"author":[{"first_name":"David","last_name":"Borthwick","full_name":"Borthwick, David"},{"orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"}],"doi":"10.4171/jst/125","publication_identifier":{"issn":["1664-039X"]},"publication_status":"published","intvolume":"         6","page":"267-329","citation":{"apa":"Borthwick, D., &#38; Weich, T. (2016). Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions. <i>Journal of Spectral Theory</i>, <i>6</i>(2), 267–329. <a href=\"https://doi.org/10.4171/jst/125\">https://doi.org/10.4171/jst/125</a>","short":"D. Borthwick, T. Weich, Journal of Spectral Theory 6 (2016) 267–329.","bibtex":"@article{Borthwick_Weich_2016, title={Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions}, volume={6}, DOI={<a href=\"https://doi.org/10.4171/jst/125\">10.4171/jst/125</a>}, number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Borthwick, David and Weich, Tobias}, year={2016}, pages={267–329} }","mla":"Borthwick, David, and Tobias Weich. “Symmetry Reduction of Holomorphic Iterated Function Schemes and Factorization of Selberg Zeta Functions.” <i>Journal of Spectral Theory</i>, vol. 6, no. 2, European Mathematical Society - EMS - Publishing House GmbH, 2016, pp. 267–329, doi:<a href=\"https://doi.org/10.4171/jst/125\">10.4171/jst/125</a>.","ieee":"D. Borthwick and T. Weich, “Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions,” <i>Journal of Spectral Theory</i>, vol. 6, no. 2, pp. 267–329, 2016, doi: <a href=\"https://doi.org/10.4171/jst/125\">10.4171/jst/125</a>.","chicago":"Borthwick, David, and Tobias Weich. “Symmetry Reduction of Holomorphic Iterated Function Schemes and Factorization of Selberg Zeta Functions.” <i>Journal of Spectral Theory</i> 6, no. 2 (2016): 267–329. <a href=\"https://doi.org/10.4171/jst/125\">https://doi.org/10.4171/jst/125</a>.","ama":"Borthwick D, Weich T. Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions. <i>Journal of Spectral Theory</i>. 2016;6(2):267-329. doi:<a href=\"https://doi.org/10.4171/jst/125\">10.4171/jst/125</a>"},"_id":"31274","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","type":"journal_article","status":"public","publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_created":"2022-05-17T12:18:22Z","title":"Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions","issue":"2","year":"2016","external_id":{"arxiv":["1407.6134 "]},"keyword":["Geometry and Topology","Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication":"Journal of Spectral Theory"},{"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","_id":"31289","status":"public","type":"journal_article","doi":"10.1007/s00023-016-0514-5","volume":18,"author":[{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"date_updated":"2022-05-19T10:15:36Z","intvolume":"        18","page":"37-52","citation":{"short":"T. Weich, Annales Henri Poincaré 18 (2016) 37–52.","mla":"Weich, Tobias. “On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows.” <i>Annales Henri Poincaré</i>, vol. 18, no. 1, Springer Science and Business Media LLC, 2016, pp. 37–52, doi:<a href=\"https://doi.org/10.1007/s00023-016-0514-5\">10.1007/s00023-016-0514-5</a>.","bibtex":"@article{Weich_2016, title={On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows}, volume={18}, DOI={<a href=\"https://doi.org/10.1007/s00023-016-0514-5\">10.1007/s00023-016-0514-5</a>}, number={1}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Weich, Tobias}, year={2016}, pages={37–52} }","apa":"Weich, T. (2016). On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows. <i>Annales Henri Poincaré</i>, <i>18</i>(1), 37–52. <a href=\"https://doi.org/10.1007/s00023-016-0514-5\">https://doi.org/10.1007/s00023-016-0514-5</a>","ama":"Weich T. On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows. <i>Annales Henri Poincaré</i>. 2016;18(1):37-52. doi:<a href=\"https://doi.org/10.1007/s00023-016-0514-5\">10.1007/s00023-016-0514-5</a>","chicago":"Weich, Tobias. “On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows.” <i>Annales Henri Poincaré</i> 18, no. 1 (2016): 37–52. <a href=\"https://doi.org/10.1007/s00023-016-0514-5\">https://doi.org/10.1007/s00023-016-0514-5</a>.","ieee":"T. Weich, “On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows,” <i>Annales Henri Poincaré</i>, vol. 18, no. 1, pp. 37–52, 2016, doi: <a href=\"https://doi.org/10.1007/s00023-016-0514-5\">10.1007/s00023-016-0514-5</a>."},"publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"external_id":{"arxiv":["1511.08338"]},"publication":"Annales Henri Poincaré","title":"On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows","date_created":"2022-05-17T12:53:51Z","publisher":"Springer Science and Business Media LLC","year":"2016","issue":"1"},{"date_updated":"2022-05-19T10:15:54Z","volume":37,"author":[{"full_name":"ARNOLDI, JEAN FRANCOIS","last_name":"ARNOLDI","first_name":"JEAN FRANCOIS"},{"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"}],"doi":"10.1017/etds.2015.34","publication_identifier":{"issn":["0143-3857","1469-4417"]},"publication_status":"published","intvolume":"        37","page":"1-58","citation":{"chicago":"ARNOLDI, JEAN FRANCOIS, FRÉDÉRIC FAURE, and Tobias Weich. “Asymptotic Spectral Gap and Weyl Law for Ruelle Resonances of Open Partially Expanding Maps.” <i>Ergodic Theory and Dynamical Systems</i> 37, no. 1 (2015): 1–58. <a href=\"https://doi.org/10.1017/etds.2015.34\">https://doi.org/10.1017/etds.2015.34</a>.","ieee":"J. F. ARNOLDI, F. FAURE, and T. Weich, “Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 37, no. 1, pp. 1–58, 2015, doi: <a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>.","ama":"ARNOLDI JF, FAURE F, Weich T. Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps. <i>Ergodic Theory and Dynamical Systems</i>. 2015;37(1):1-58. doi:<a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>","apa":"ARNOLDI, J. F., FAURE, F., &#38; Weich, T. (2015). Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps. <i>Ergodic Theory and Dynamical Systems</i>, <i>37</i>(1), 1–58. <a href=\"https://doi.org/10.1017/etds.2015.34\">https://doi.org/10.1017/etds.2015.34</a>","bibtex":"@article{ARNOLDI_FAURE_Weich_2015, title={Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps}, volume={37}, DOI={<a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>}, number={1}, journal={Ergodic Theory and Dynamical Systems}, publisher={Cambridge University Press (CUP)}, author={ARNOLDI, JEAN FRANCOIS and FAURE, FRÉDÉRIC and Weich, Tobias}, year={2015}, pages={1–58} }","mla":"ARNOLDI, JEAN FRANCOIS, et al. “Asymptotic Spectral Gap and Weyl Law for Ruelle Resonances of Open Partially Expanding Maps.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 37, no. 1, Cambridge University Press (CUP), 2015, pp. 1–58, doi:<a href=\"https://doi.org/10.1017/etds.2015.34\">10.1017/etds.2015.34</a>.","short":"J.F. ARNOLDI, F. FAURE, T. Weich, Ergodic Theory and Dynamical Systems 37 (2015) 1–58."},"_id":"31291","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","type":"journal_article","status":"public","publisher":"Cambridge University Press (CUP)","date_created":"2022-05-17T12:55:26Z","title":"Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps","issue":"1","year":"2015","external_id":{"arxiv":["1302.3087"]},"keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publication":"Ergodic Theory and Dynamical Systems","abstract":[{"lang":"eng","text":"<jats:p>We consider a simple model of an open partially expanding map. Its trapped set <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline1\" /><jats:tex-math>${\\mathcal{K}}$</jats:tex-math></jats:alternatives></jats:inline-formula> in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline2\" /><jats:tex-math>$\\unicode[STIX]{x1D708}$</jats:tex-math></jats:alternatives></jats:inline-formula> in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis is stable under perturbations and means that the dynamics is univalued in a neighborhood of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline3\" /><jats:tex-math>${\\mathcal{K}}$</jats:tex-math></jats:alternatives></jats:inline-formula>. Under this hypothesis we show the existence of an asymptotic spectral gap and a fractal Weyl law for the upper bound of density of Ruelle resonances in the semiclassical limit <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0143385715000346_inline4\" /><jats:tex-math>$\\unicode[STIX]{x1D708}\\rightarrow \\infty$</jats:tex-math></jats:alternatives></jats:inline-formula>. Some numerical computations with the truncated Gauss map and Bowen–Series maps illustrate these results.</jats:p>"}]},{"external_id":{"arxiv":["1403.7419 "]},"language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publication":"Communications in Mathematical Physics","date_created":"2022-05-17T12:56:21Z","publisher":"Springer Science and Business Media LLC","title":"Resonance Chains and Geometric Limits on Schottky Surfaces","issue":"2","year":"2015","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","_id":"31293","type":"journal_article","status":"public","volume":337,"author":[{"first_name":"Tobias","full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"date_updated":"2022-05-19T10:16:21Z","doi":"10.1007/s00220-015-2359-z","publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","intvolume":"       337","page":"727-765","citation":{"mla":"Weich, Tobias. “Resonance Chains and Geometric Limits on Schottky Surfaces.” <i>Communications in Mathematical Physics</i>, vol. 337, no. 2, Springer Science and Business Media LLC, 2015, pp. 727–65, doi:<a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>.","bibtex":"@article{Weich_2015, title={Resonance Chains and Geometric Limits on Schottky Surfaces}, volume={337}, DOI={<a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Weich, Tobias}, year={2015}, pages={727–765} }","short":"T. Weich, Communications in Mathematical Physics 337 (2015) 727–765.","apa":"Weich, T. (2015). Resonance Chains and Geometric Limits on Schottky Surfaces. <i>Communications in Mathematical Physics</i>, <i>337</i>(2), 727–765. <a href=\"https://doi.org/10.1007/s00220-015-2359-z\">https://doi.org/10.1007/s00220-015-2359-z</a>","ama":"Weich T. Resonance Chains and Geometric Limits on Schottky Surfaces. <i>Communications in Mathematical Physics</i>. 2015;337(2):727-765. doi:<a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>","chicago":"Weich, Tobias. “Resonance Chains and Geometric Limits on Schottky Surfaces.” <i>Communications in Mathematical Physics</i> 337, no. 2 (2015): 727–65. <a href=\"https://doi.org/10.1007/s00220-015-2359-z\">https://doi.org/10.1007/s00220-015-2359-z</a>.","ieee":"T. Weich, “Resonance Chains and Geometric Limits on Schottky Surfaces,” <i>Communications in Mathematical Physics</i>, vol. 337, no. 2, pp. 727–765, 2015, doi: <a href=\"https://doi.org/10.1007/s00220-015-2359-z\">10.1007/s00220-015-2359-z</a>."}},{"type":"journal_article","status":"public","_id":"31294","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","article_number":"101501","publication_identifier":{"issn":["0022-2488","1089-7658"]},"publication_status":"published","intvolume":"        55","citation":{"bibtex":"@article{Weich_2014, title={Equivariant spectral asymptotics for<i>h</i>-pseudodifferential operators}, volume={55}, DOI={<a href=\"https://doi.org/10.1063/1.4896698\">10.1063/1.4896698</a>}, number={10101501}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Weich, Tobias}, year={2014} }","short":"T. Weich, Journal of Mathematical Physics 55 (2014).","mla":"Weich, Tobias. “Equivariant Spectral Asymptotics for<i>h</i>-Pseudodifferential Operators.” <i>Journal of Mathematical Physics</i>, vol. 55, no. 10, 101501, AIP Publishing, 2014, doi:<a href=\"https://doi.org/10.1063/1.4896698\">10.1063/1.4896698</a>.","apa":"Weich, T. (2014). Equivariant spectral asymptotics for<i>h</i>-pseudodifferential operators. <i>Journal of Mathematical Physics</i>, <i>55</i>(10), Article 101501. <a href=\"https://doi.org/10.1063/1.4896698\">https://doi.org/10.1063/1.4896698</a>","chicago":"Weich, Tobias. “Equivariant Spectral Asymptotics for<i>h</i>-Pseudodifferential Operators.” <i>Journal of Mathematical Physics</i> 55, no. 10 (2014). <a href=\"https://doi.org/10.1063/1.4896698\">https://doi.org/10.1063/1.4896698</a>.","ieee":"T. Weich, “Equivariant spectral asymptotics for<i>h</i>-pseudodifferential operators,” <i>Journal of Mathematical Physics</i>, vol. 55, no. 10, Art. no. 101501, 2014, doi: <a href=\"https://doi.org/10.1063/1.4896698\">10.1063/1.4896698</a>.","ama":"Weich T. Equivariant spectral asymptotics for<i>h</i>-pseudodifferential operators. <i>Journal of Mathematical Physics</i>. 2014;55(10). doi:<a href=\"https://doi.org/10.1063/1.4896698\">10.1063/1.4896698</a>"},"date_updated":"2022-05-19T10:16:38Z","volume":55,"author":[{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias"}],"doi":"10.1063/1.4896698","publication":"Journal of Mathematical Physics","external_id":{"arxiv":["1311.2436 "]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"issue":"10","year":"2014","publisher":"AIP Publishing","date_created":"2022-05-17T12:57:00Z","title":"Equivariant spectral asymptotics for<i>h</i>-pseudodifferential operators"},{"publication":"Nonlinearity","keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1403.7771 "]},"year":"2014","issue":"8","title":"Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum","publisher":"IOP Publishing","date_created":"2022-05-17T12:58:25Z","status":"public","type":"journal_article","_id":"31296","user_id":"48188","department":[{"_id":"10"},{"_id":"548"},{"_id":"288"}],"citation":{"ama":"Barkhofen S, Faure F, Weich T. Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum. <i>Nonlinearity</i>. 2014;27(8):1829-1858. doi:<a href=\"https://doi.org/10.1088/0951-7715/27/8/1829\">10.1088/0951-7715/27/8/1829</a>","chicago":"Barkhofen, Sonja, F Faure, and Tobias Weich. “Resonance Chains in Open Systems, Generalized Zeta Functions and Clustering of the Length Spectrum.” <i>Nonlinearity</i> 27, no. 8 (2014): 1829–58. <a href=\"https://doi.org/10.1088/0951-7715/27/8/1829\">https://doi.org/10.1088/0951-7715/27/8/1829</a>.","ieee":"S. Barkhofen, F. Faure, and T. Weich, “Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum,” <i>Nonlinearity</i>, vol. 27, no. 8, pp. 1829–1858, 2014, doi: <a href=\"https://doi.org/10.1088/0951-7715/27/8/1829\">10.1088/0951-7715/27/8/1829</a>.","mla":"Barkhofen, Sonja, et al. “Resonance Chains in Open Systems, Generalized Zeta Functions and Clustering of the Length Spectrum.” <i>Nonlinearity</i>, vol. 27, no. 8, IOP Publishing, 2014, pp. 1829–58, doi:<a href=\"https://doi.org/10.1088/0951-7715/27/8/1829\">10.1088/0951-7715/27/8/1829</a>.","short":"S. Barkhofen, F. Faure, T. Weich, Nonlinearity 27 (2014) 1829–1858.","bibtex":"@article{Barkhofen_Faure_Weich_2014, title={Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum}, volume={27}, DOI={<a href=\"https://doi.org/10.1088/0951-7715/27/8/1829\">10.1088/0951-7715/27/8/1829</a>}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Barkhofen, Sonja and Faure, F and Weich, Tobias}, year={2014}, pages={1829–1858} }","apa":"Barkhofen, S., Faure, F., &#38; Weich, T. (2014). Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum. <i>Nonlinearity</i>, <i>27</i>(8), 1829–1858. <a href=\"https://doi.org/10.1088/0951-7715/27/8/1829\">https://doi.org/10.1088/0951-7715/27/8/1829</a>"},"page":"1829-1858","intvolume":"        27","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"doi":"10.1088/0951-7715/27/8/1829","date_updated":"2023-01-19T08:56:12Z","author":[{"full_name":"Barkhofen, Sonja","id":"48188","last_name":"Barkhofen","first_name":"Sonja"},{"first_name":"F","last_name":"Faure","full_name":"Faure, F"},{"orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"}],"volume":27},{"year":"2014","issue":"3","title":"Formation and interaction of resonance chains in the open three-disk system","date_created":"2022-05-17T12:59:49Z","publisher":"IOP Publishing","publication":"New Journal of Physics","language":[{"iso":"eng"}],"keyword":["General Physics and Astronomy"],"external_id":{"arxiv":["1311.5128 "]},"intvolume":"        16","citation":{"ieee":"T. Weich, S. Barkhofen, U. Kuhl, C. Poli, and H. Schomerus, “Formation and interaction of resonance chains in the open three-disk system,” <i>New Journal of Physics</i>, vol. 16, no. 3, Art. no. 033029, 2014, doi: <a href=\"https://doi.org/10.1088/1367-2630/16/3/033029\">10.1088/1367-2630/16/3/033029</a>.","chicago":"Weich, Tobias, Sonja Barkhofen, U Kuhl, C Poli, and H Schomerus. “Formation and Interaction of Resonance Chains in the Open Three-Disk System.” <i>New Journal of Physics</i> 16, no. 3 (2014). <a href=\"https://doi.org/10.1088/1367-2630/16/3/033029\">https://doi.org/10.1088/1367-2630/16/3/033029</a>.","ama":"Weich T, Barkhofen S, Kuhl U, Poli C, Schomerus H. Formation and interaction of resonance chains in the open three-disk system. <i>New Journal of Physics</i>. 2014;16(3). doi:<a href=\"https://doi.org/10.1088/1367-2630/16/3/033029\">10.1088/1367-2630/16/3/033029</a>","apa":"Weich, T., Barkhofen, S., Kuhl, U., Poli, C., &#38; Schomerus, H. (2014). Formation and interaction of resonance chains in the open three-disk system. <i>New Journal of Physics</i>, <i>16</i>(3), Article 033029. <a href=\"https://doi.org/10.1088/1367-2630/16/3/033029\">https://doi.org/10.1088/1367-2630/16/3/033029</a>","bibtex":"@article{Weich_Barkhofen_Kuhl_Poli_Schomerus_2014, title={Formation and interaction of resonance chains in the open three-disk system}, volume={16}, DOI={<a href=\"https://doi.org/10.1088/1367-2630/16/3/033029\">10.1088/1367-2630/16/3/033029</a>}, number={3033029}, journal={New Journal of Physics}, publisher={IOP Publishing}, author={Weich, Tobias and Barkhofen, Sonja and Kuhl, U and Poli, C and Schomerus, H}, year={2014} }","short":"T. Weich, S. Barkhofen, U. Kuhl, C. Poli, H. Schomerus, New Journal of Physics 16 (2014).","mla":"Weich, Tobias, et al. “Formation and Interaction of Resonance Chains in the Open Three-Disk System.” <i>New Journal of Physics</i>, vol. 16, no. 3, 033029, IOP Publishing, 2014, doi:<a href=\"https://doi.org/10.1088/1367-2630/16/3/033029\">10.1088/1367-2630/16/3/033029</a>."},"publication_identifier":{"issn":["1367-2630"]},"publication_status":"published","doi":"10.1088/1367-2630/16/3/033029","volume":16,"author":[{"last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"},{"first_name":"Sonja","last_name":"Barkhofen","id":"48188","full_name":"Barkhofen, Sonja"},{"full_name":"Kuhl, U","last_name":"Kuhl","first_name":"U"},{"first_name":"C","last_name":"Poli","full_name":"Poli, C"},{"first_name":"H","full_name":"Schomerus, H","last_name":"Schomerus"}],"date_updated":"2023-01-24T08:07:57Z","status":"public","type":"journal_article","article_number":"033029","department":[{"_id":"10"},{"_id":"548"}],"user_id":"48188","_id":"31297"},{"issue":"16","year":"2013","date_created":"2022-05-17T13:00:47Z","publisher":"American Physical Society (APS)","title":"Experimental Observation of the Spectral Gap in Microwave n-Disk Systems","publication":"Physical Review Letters","external_id":{"arxiv":["1212.5897 "]},"language":[{"iso":"eng"}],"keyword":["General Physics and Astronomy"],"publication_status":"published","publication_identifier":{"issn":["0031-9007","1079-7114"]},"citation":{"ama":"Barkhofen S, Weich T, Potzuweit A, Stöckmann H-J, Kuhl U, Zworski M. Experimental Observation of the Spectral Gap in Microwave n-Disk Systems. <i>Physical Review Letters</i>. 2013;110(16). doi:<a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>","chicago":"Barkhofen, Sonja, Tobias Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, and M. Zworski. “Experimental Observation of the Spectral Gap in Microwave N-Disk Systems.” <i>Physical Review Letters</i> 110, no. 16 (2013). <a href=\"https://doi.org/10.1103/physrevlett.110.164102\">https://doi.org/10.1103/physrevlett.110.164102</a>.","ieee":"S. Barkhofen, T. Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, and M. Zworski, “Experimental Observation of the Spectral Gap in Microwave n-Disk Systems,” <i>Physical Review Letters</i>, vol. 110, no. 16, Art. no. 164102, 2013, doi: <a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>.","apa":"Barkhofen, S., Weich, T., Potzuweit, A., Stöckmann, H.-J., Kuhl, U., &#38; Zworski, M. (2013). Experimental Observation of the Spectral Gap in Microwave n-Disk Systems. <i>Physical Review Letters</i>, <i>110</i>(16), Article 164102. <a href=\"https://doi.org/10.1103/physrevlett.110.164102\">https://doi.org/10.1103/physrevlett.110.164102</a>","mla":"Barkhofen, Sonja, et al. “Experimental Observation of the Spectral Gap in Microwave N-Disk Systems.” <i>Physical Review Letters</i>, vol. 110, no. 16, 164102, American Physical Society (APS), 2013, doi:<a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>.","bibtex":"@article{Barkhofen_Weich_Potzuweit_Stöckmann_Kuhl_Zworski_2013, title={Experimental Observation of the Spectral Gap in Microwave n-Disk Systems}, volume={110}, DOI={<a href=\"https://doi.org/10.1103/physrevlett.110.164102\">10.1103/physrevlett.110.164102</a>}, number={16164102}, journal={Physical Review Letters}, publisher={American Physical Society (APS)}, author={Barkhofen, Sonja and Weich, Tobias and Potzuweit, A. and Stöckmann, H.-J. and Kuhl, U. and Zworski, M.}, year={2013} }","short":"S. Barkhofen, T. Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, M. Zworski, Physical Review Letters 110 (2013)."},"intvolume":"       110","author":[{"last_name":"Barkhofen","id":"48188","full_name":"Barkhofen, Sonja","first_name":"Sonja"},{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"first_name":"A.","last_name":"Potzuweit","full_name":"Potzuweit, A."},{"first_name":"H.-J.","full_name":"Stöckmann, H.-J.","last_name":"Stöckmann"},{"last_name":"Kuhl","full_name":"Kuhl, U.","first_name":"U."},{"first_name":"M.","last_name":"Zworski","full_name":"Zworski, M."}],"volume":110,"date_updated":"2023-01-19T08:49:01Z","doi":"10.1103/physrevlett.110.164102","type":"journal_article","status":"public","user_id":"48188","department":[{"_id":"10"},{"_id":"548"},{"_id":"288"}],"_id":"31298","article_number":"164102"},{"publisher":"American Physical Society (APS)","date_created":"2022-05-17T13:01:39Z","title":"Weyl asymptotics: From closed to open systems","issue":"6","year":"2012","external_id":{"arxiv":["1209.2304"]},"keyword":["Industrial and Manufacturing Engineering","Metals and Alloys","Strategy and Management","Mechanical Engineering"],"language":[{"iso":"eng"}],"publication":"Physical Review E","date_updated":"2022-05-19T10:18:57Z","author":[{"first_name":"A.","last_name":"Potzuweit","full_name":"Potzuweit, A."},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias"},{"first_name":"Sonja","last_name":"Barkhofen","full_name":"Barkhofen, Sonja","id":"48188"},{"last_name":"Kuhl","full_name":"Kuhl, U.","first_name":"U."},{"last_name":"Stöckmann","full_name":"Stöckmann, H.-J.","first_name":"H.-J."},{"last_name":"Zworski","full_name":"Zworski, M.","first_name":"M."}],"volume":86,"doi":"10.1103/physreve.86.066205","publication_status":"published","publication_identifier":{"issn":["1539-3755","1550-2376"]},"citation":{"mla":"Potzuweit, A., et al. “Weyl Asymptotics: From Closed to Open Systems.” <i>Physical Review E</i>, vol. 86, no. 6, 066205, American Physical Society (APS), 2012, doi:<a href=\"https://doi.org/10.1103/physreve.86.066205\">10.1103/physreve.86.066205</a>.","bibtex":"@article{Potzuweit_Weich_Barkhofen_Kuhl_Stöckmann_Zworski_2012, title={Weyl asymptotics: From closed to open systems}, volume={86}, DOI={<a href=\"https://doi.org/10.1103/physreve.86.066205\">10.1103/physreve.86.066205</a>}, number={6066205}, journal={Physical Review E}, publisher={American Physical Society (APS)}, author={Potzuweit, A. and Weich, Tobias and Barkhofen, Sonja and Kuhl, U. and Stöckmann, H.-J. and Zworski, M.}, year={2012} }","short":"A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H.-J. Stöckmann, M. Zworski, Physical Review E 86 (2012).","apa":"Potzuweit, A., Weich, T., Barkhofen, S., Kuhl, U., Stöckmann, H.-J., &#38; Zworski, M. (2012). Weyl asymptotics: From closed to open systems. <i>Physical Review E</i>, <i>86</i>(6), Article 066205. <a href=\"https://doi.org/10.1103/physreve.86.066205\">https://doi.org/10.1103/physreve.86.066205</a>","ama":"Potzuweit A, Weich T, Barkhofen S, Kuhl U, Stöckmann H-J, Zworski M. Weyl asymptotics: From closed to open systems. <i>Physical Review E</i>. 2012;86(6). doi:<a href=\"https://doi.org/10.1103/physreve.86.066205\">10.1103/physreve.86.066205</a>","chicago":"Potzuweit, A., Tobias Weich, Sonja Barkhofen, U. Kuhl, H.-J. Stöckmann, and M. Zworski. “Weyl Asymptotics: From Closed to Open Systems.” <i>Physical Review E</i> 86, no. 6 (2012). <a href=\"https://doi.org/10.1103/physreve.86.066205\">https://doi.org/10.1103/physreve.86.066205</a>.","ieee":"A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H.-J. Stöckmann, and M. Zworski, “Weyl asymptotics: From closed to open systems,” <i>Physical Review E</i>, vol. 86, no. 6, Art. no. 066205, 2012, doi: <a href=\"https://doi.org/10.1103/physreve.86.066205\">10.1103/physreve.86.066205</a>."},"intvolume":"        86","_id":"31300","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"article_number":"066205","type":"journal_article","status":"public"}]