[{"doi":"10.1016/j.indag.2023.02.003","title":"Decompositions of Analytic 1-Manifolds","date_created":"2022-12-22T09:46:36Z","author":[{"first_name":"Maximilian","full_name":"Hanusch, Maximilian","id":"30905","last_name":"Hanusch"}],"volume":34,"date_updated":"2023-05-25T07:32:38Z","citation":{"mla":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes Mathematicae.</i>, vol. 34, no. 4, 2023, pp. 752–811, doi:<a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>.","bibtex":"@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds}, volume={34}, DOI={<a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>}, number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian}, year={2023}, pages={752–811} }","short":"M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.","apa":"Hanusch, M. (2023). Decompositions of Analytic 1-Manifolds. <i>Indagationes Mathematicae.</i>, <i>34</i>(4), 752–811. <a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">https://doi.org/10.1016/j.indag.2023.02.003</a>","ieee":"M. Hanusch, “Decompositions of Analytic 1-Manifolds,” <i>Indagationes Mathematicae.</i>, vol. 34, no. 4, pp. 752–811, 2023, doi: <a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>.","chicago":"Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes Mathematicae.</i> 34, no. 4 (2023): 752–811. <a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">https://doi.org/10.1016/j.indag.2023.02.003</a>.","ama":"Hanusch M. Decompositions of Analytic 1-Manifolds. <i>Indagationes Mathematicae</i>. 2023;34(4):752-811. doi:<a href=\"https://doi.org/10.1016/j.indag.2023.02.003\">10.1016/j.indag.2023.02.003</a>"},"intvolume":"        34","page":"752-811","year":"2023","issue":"4","publication_status":"published","language":[{"iso":"eng"}],"keyword":["Lie group actions and analytic 1-submanifolds"],"user_id":"30905","department":[{"_id":"93"}],"_id":"34833","status":"public","type":"journal_article","publication":"Indagationes Mathematicae."},{"date_created":"2026-01-16T08:39:40Z","publisher":"Springer Science and Business Media LLC","title":"Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions","issue":"6","year":"2023","external_id":{"arxiv":["2211.14046"]},"language":[{"iso":"eng"}],"publication":"Annales Henri Poincaré","volume":25,"author":[{"first_name":"Benjamin","orcid":"0000-0001-9074-1205","last_name":"Hinrichs","full_name":"Hinrichs, Benjamin","id":"99427"},{"last_name":"Matte","full_name":"Matte, Oliver","first_name":"Oliver"}],"date_updated":"2026-01-16T09:05:26Z","oa":"1","doi":"10.1007/s00023-023-01369-z","main_file_link":[{"open_access":"1"}],"publication_identifier":{"issn":["1424-0637","1424-0661"]},"publication_status":"published","intvolume":"        25","page":"2877-2940","citation":{"ama":"Hinrichs B, Matte O. Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions. <i>Annales Henri Poincaré</i>. 2023;25(6):2877-2940. doi:<a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.” <i>Annales Henri Poincaré</i> 25, no. 6 (2023): 2877–2940. <a href=\"https://doi.org/10.1007/s00023-023-01369-z\">https://doi.org/10.1007/s00023-023-01369-z</a>.","ieee":"B. Hinrichs and O. Matte, “Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions,” <i>Annales Henri Poincaré</i>, vol. 25, no. 6, pp. 2877–2940, 2023, doi: <a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>.","mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.” <i>Annales Henri Poincaré</i>, vol. 25, no. 6, Springer Science and Business Media LLC, 2023, pp. 2877–940, doi:<a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>.","short":"B. Hinrichs, O. Matte, Annales Henri Poincaré 25 (2023) 2877–2940.","bibtex":"@article{Hinrichs_Matte_2023, title={Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions}, volume={25}, DOI={<a href=\"https://doi.org/10.1007/s00023-023-01369-z\">10.1007/s00023-023-01369-z</a>}, number={6}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023}, pages={2877–2940} }","apa":"Hinrichs, B., &#38; Matte, O. (2023). Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions. <i>Annales Henri Poincaré</i>, <i>25</i>(6), 2877–2940. <a href=\"https://doi.org/10.1007/s00023-023-01369-z\">https://doi.org/10.1007/s00023-023-01369-z</a>"},"department":[{"_id":"799"}],"user_id":"99427","_id":"63635","extern":"1","article_type":"original","type":"journal_article","status":"public"},{"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Analysis"],"external_id":{"arxiv":["2205.09189"]},"publication":"Journal of Mathematical Analysis and Applications","title":"Super-Gaussian decay of exponentials: A sufficient condition","date_created":"2023-07-20T05:08:49Z","publisher":"Elsevier BV","year":"2023","issue":"1","article_number":"127558","department":[{"_id":"799"}],"user_id":"99427","_id":"46100","status":"public","type":"journal_article","doi":"10.1016/j.jmaa.2023.127558","main_file_link":[{"open_access":"1"}],"volume":528,"author":[{"first_name":"Benjamin","orcid":"0000-0001-9074-1205","last_name":"Hinrichs","id":"99427","full_name":"Hinrichs, Benjamin"},{"first_name":"Daan W.","full_name":"Janssen, Daan W.","last_name":"Janssen"},{"first_name":"Jobst","full_name":"Ziebell, Jobst","last_name":"Ziebell"}],"date_updated":"2026-01-16T09:04:39Z","oa":"1","intvolume":"       528","citation":{"ama":"Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A sufficient condition. <i>Journal of Mathematical Analysis and Applications</i>. 2023;528(1). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>","chicago":"Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” <i>Journal of Mathematical Analysis and Applications</i> 528, no. 1 (2023). <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">https://doi.org/10.1016/j.jmaa.2023.127558</a>.","ieee":"B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials: A sufficient condition,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 528, no. 1, Art. no. 127558, 2023, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>.","mla":"Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient Condition.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 528, no. 1, 127558, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>.","short":"B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and Applications 528 (2023).","bibtex":"@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of exponentials: A sufficient condition}, volume={528}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">10.1016/j.jmaa.2023.127558</a>}, number={1127558}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}, year={2023} }","apa":"Hinrichs, B., Janssen, D. W., &#38; Ziebell, J. (2023). Super-Gaussian decay of exponentials: A sufficient condition. <i>Journal of Mathematical Analysis and Applications</i>, <i>528</i>(1), Article 127558. <a href=\"https://doi.org/10.1016/j.jmaa.2023.127558\">https://doi.org/10.1016/j.jmaa.2023.127558</a>"},"publication_identifier":{"issn":["0022-247X"]},"publication_status":"published"},{"publisher":"MSP","date_created":"2022-05-11T10:41:35Z","title":"Higher rank quantum-classical correspondence","issue":"10","year":"2023","external_id":{"arxiv":["2103.05667"]},"language":[{"iso":"eng"}],"publication":"Analysis & PDE","abstract":[{"lang":"eng","text":"For a compact Riemannian locally symmetric space $\\Gamma\\backslash G/K$ of\r\narbitrary rank we determine the location of certain Ruelle-Taylor resonances\r\nfor the Weyl chamber action. We provide a Weyl-lower bound on an appropriate\r\ncounting function for the Ruelle-Taylor resonances and establish a spectral gap\r\nwhich is uniform in $\\Gamma$ if $G/K$ is irreducible of higher rank. This is\r\nachieved by proving a quantum-classical correspondence, i.e. a\r\n1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant\r\nstates and joint eigenfunctions of the algebra of invariant differential\r\noperators on $G/K$."}],"date_updated":"2026-02-18T10:39:36Z","author":[{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"},{"first_name":"Lasse Lennart","last_name":"Wolf","orcid":"0000-0001-8893-2045","id":"45027","full_name":"Wolf, Lasse Lennart"}],"volume":16,"doi":"https://doi.org/10.2140/apde.2023.16.2241","citation":{"ama":"Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence. <i>Analysis &#38; PDE</i>. 2023;16(10):2241–2265. doi:<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>","ieee":"J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,” <i>Analysis &#38; PDE</i>, vol. 16, no. 10, pp. 2241–2265, 2023, doi: <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","chicago":"Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical Correspondence.” <i>Analysis &#38; PDE</i> 16, no. 10 (2023): 2241–2265. <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","apa":"Hilgert, J., Weich, T., &#38; Wolf, L. L. (2023). Higher rank quantum-classical correspondence. <i>Analysis &#38; PDE</i>, <i>16</i>(10), 2241–2265. <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>","short":"J. Hilgert, T. Weich, L.L. Wolf, Analysis &#38; PDE 16 (2023) 2241–2265.","bibtex":"@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical correspondence}, volume={16}, DOI={<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>}, number={10}, journal={Analysis &#38; PDE}, publisher={MSP}, author={Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }","mla":"Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” <i>Analysis &#38; PDE</i>, vol. 16, no. 10, MSP, 2023, pp. 2241–2265, doi:<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>."},"page":"2241–2265","intvolume":"        16","_id":"31190","user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"type":"journal_article","status":"public"},{"date_updated":"2026-02-18T10:41:07Z","author":[{"first_name":"Philipp","last_name":"Schütte","full_name":"Schütte, Philipp","id":"50168"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias"},{"first_name":"Sonja","full_name":"Barkhofen, Sonja","id":"48188","last_name":"Barkhofen"}],"date_created":"2022-05-04T12:27:46Z","volume":398,"title":"Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems","doi":"https://doi.org/10.1007/s00220-022-04538-z","year":"2023","citation":{"short":"P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics 398 (2023) 655–678.","bibtex":"@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>}, journal={Communications in Mathematical Physics}, author={Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }","mla":"Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i>, vol. 398, 2023, pp. 655–78, doi:<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>.","apa":"Schütte, P., Weich, T., &#38; Barkhofen, S. (2023). Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>, <i>398</i>, 655–678. <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>","chicago":"Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i> 398 (2023): 655–78. <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>.","ieee":"P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems,” <i>Communications in Mathematical Physics</i>, vol. 398, pp. 655–678, 2023, doi: <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>.","ama":"Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>. 2023;398:655-678. doi:<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>"},"intvolume":"       398","page":"655-678","_id":"31059","external_id":{"arxiv":["2112.05791"]},"user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"},{"_id":"15"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Communications in Mathematical Physics","abstract":[{"lang":"eng","text":"In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems."}],"status":"public"},{"title":"Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters","date_updated":"2026-03-31T08:26:09Z","volume":10,"author":[{"full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert","first_name":"Joachim"},{"first_name":"C.","full_name":"Arends, C.","last_name":"Arends"}],"date_created":"2024-02-19T06:34:11Z","year":"2023","page":"335-403","intvolume":"        10","citation":{"ieee":"J. Hilgert and C. Arends, “Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters,” <i>J. de l’École polytechnique — Mathématiques</i>, vol. 10, pp. 335–403, 2023.","chicago":"Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally Symmetric Spaces - The Case of Exceptional Parameters.” <i>J. de l’École Polytechnique — Mathématiques</i> 10 (2023): 335–403.","ama":"Hilgert J, Arends C. Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters. <i>J de l’École polytechnique — Mathématiques</i>. 2023;10:335-403.","apa":"Hilgert, J., &#38; Arends, C. (2023). Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters. <i>J. de l’École Polytechnique — Mathématiques</i>, <i>10</i>, 335–403.","short":"J. Hilgert, C. Arends, J. de l’École Polytechnique — Mathématiques 10 (2023) 335–403.","mla":"Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally Symmetric Spaces - The Case of Exceptional Parameters.” <i>J. de l’École Polytechnique — Mathématiques</i>, vol. 10, 2023, pp. 335–403.","bibtex":"@article{Hilgert_Arends_2023, title={Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}, volume={10}, journal={J. de l’École polytechnique — Mathématiques}, author={Hilgert, Joachim and Arends, C.}, year={2023}, pages={335–403} }"},"publication_status":"published","language":[{"iso":"eng"}],"_id":"51383","department":[{"_id":"91"}],"user_id":"220","status":"public","publication":"J. de l'École polytechnique — Mathématiques","type":"journal_article"},{"status":"public","type":"journal_article","publication":"J. Diff. Equations","language":[{"iso":"eng"}],"_id":"51384","user_id":"220","department":[{"_id":"91"}],"year":"2023","citation":{"ama":"Hilgert J, Glöckner H. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. <i>J Diff Equations</i>. 2023;343:186-232.","chicago":"Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” <i>J. Diff. Equations</i> 343 (2023): 186–232.","ieee":"J. Hilgert and H. Glöckner, “Aspects of control theory on infinite-dimensional Lie groups and G-manifolds,” <i>J. Diff. Equations</i>, vol. 343, pp. 186–232, 2023.","apa":"Hilgert, J., &#38; Glöckner, H. (2023). Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. <i>J. Diff. Equations</i>, <i>343</i>, 186–232.","mla":"Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional Lie Groups and G-Manifolds.” <i>J. Diff. Equations</i>, vol. 343, 2023, pp. 186–232.","bibtex":"@article{Hilgert_Glöckner_2023, title={Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}, volume={343}, journal={J. Diff. Equations}, author={Hilgert, Joachim and Glöckner, H.}, year={2023}, pages={186–232} }","short":"J. Hilgert, H. Glöckner, J. Diff. Equations 343 (2023) 186–232."},"page":"186-232","intvolume":"       343","publication_status":"published","title":"Aspects of control theory on infinite-dimensional Lie groups and G-manifolds","date_updated":"2026-03-31T08:25:53Z","author":[{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"},{"full_name":"Glöckner, H.","last_name":"Glöckner","first_name":"H."}],"date_created":"2024-02-19T06:35:08Z","volume":343},{"_id":"31982","user_id":"70575","department":[{"_id":"548"}],"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Inventiones mathematicae","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with Betti number <jats:inline-formula><jats:alternatives><jats:tex-math>$$b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mi>b</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:msub>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, the order of vanishing of the Ruelle zeta function at zero equals <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, while in the hyperbolic case it is equal to <jats:inline-formula><jats:alternatives><jats:tex-math>$$4-2b_1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mn>4</mml:mn>\r\n                    <mml:mo>-</mml:mo>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:msub>\r\n                      <mml:mi>b</mml:mi>\r\n                      <mml:mn>1</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>Σ</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with harmonic 1-forms on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Sigma $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Σ</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>","lang":"eng"}],"status":"public","publisher":"Springer Science and Business Media LLC","date_updated":"2022-06-21T11:55:15Z","date_created":"2022-06-20T08:24:17Z","author":[{"last_name":"Cekić","full_name":"Cekić, Mihajlo","first_name":"Mihajlo"},{"last_name":"Delarue","full_name":"Delarue, Benjamin","id":"70575","first_name":"Benjamin"},{"full_name":"Dyatlov, Semyon","last_name":"Dyatlov","first_name":"Semyon"},{"first_name":"Gabriel P.","last_name":"Paternain","full_name":"Paternain, Gabriel P."}],"volume":229,"title":"The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds","doi":"10.1007/s00222-022-01108-x","publication_status":"published","publication_identifier":{"issn":["0020-9910","1432-1297"]},"issue":"1","year":"2022","citation":{"ama":"Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones mathematicae</i>. 2022;229(1):303-394. doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>","ieee":"M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds,” <i>Inventiones mathematicae</i>, vol. 229, no. 1, pp. 303–394, 2022, doi: <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>.","chicago":"Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i> 229, no. 1 (2022): 303–94. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>.","apa":"Cekić, M., Delarue, B., Dyatlov, S., &#38; Paternain, G. P. (2022). The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. <i>Inventiones Mathematicae</i>, <i>229</i>(1), 303–394. <a href=\"https://doi.org/10.1007/s00222-022-01108-x\">https://doi.org/10.1007/s00222-022-01108-x</a>","bibtex":"@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>}, number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }","short":"M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394.","mla":"Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” <i>Inventiones Mathematicae</i>, vol. 229, no. 1, Springer Science and Business Media LLC, 2022, pp. 303–94, doi:<a href=\"https://doi.org/10.1007/s00222-022-01108-x\">10.1007/s00222-022-01108-x</a>."},"page":"303-394","intvolume":"       229"},{"status":"public","type":"journal_article","publication":"p-Adic Numbers, Ultrametric Analysis, and Applications","language":[{"iso":"eng"}],"article_type":"original","keyword":["20Exx","22Exx","32Cxx"],"user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34792","citation":{"ama":"Glöckner H. Non-Lie subgroups in Lie groups over local fields of positive characteristic. <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>. 2022;14(2):138–144. doi:<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>","chicago":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i> 14, no. 2 (2022): 138–144. <a href=\"https://doi.org/10.1134/S2070046622020042\">https://doi.org/10.1134/S2070046622020042</a>.","ieee":"H. Glöckner, “Non-Lie subgroups in Lie groups over local fields of positive characteristic,” <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>, vol. 14, no. 2, pp. 138–144, 2022, doi: <a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>.","mla":"Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>, vol. 14, no. 2, 2022, pp. 138–144, doi:<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>.","short":"H. Glöckner, P-Adic Numbers, Ultrametric Analysis, and Applications 14 (2022) 138–144.","bibtex":"@article{Glöckner_2022, title={Non-Lie subgroups in Lie groups over local fields of positive characteristic}, volume={14}, DOI={<a href=\"https://doi.org/10.1134/S2070046622020042\">10.1134/S2070046622020042</a>}, number={2}, journal={p-Adic Numbers, Ultrametric Analysis, and Applications}, author={Glöckner, Helge}, year={2022}, pages={138–144} }","apa":"Glöckner, H. (2022). Non-Lie subgroups in Lie groups over local fields of positive characteristic. <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>, <i>14</i>(2), 138–144. <a href=\"https://doi.org/10.1134/S2070046622020042\">https://doi.org/10.1134/S2070046622020042</a>"},"intvolume":"        14","page":"138–144","year":"2022","issue":"2","publication_identifier":{"issn":["2070-0466"]},"quality_controlled":"1","doi":"10.1134/S2070046622020042","title":"Non-Lie subgroups in Lie groups over local fields of positive characteristic","author":[{"first_name":"Helge","full_name":"Glöckner, Helge","id":"178","last_name":"Glöckner"}],"date_created":"2022-12-21T19:27:51Z","volume":14,"date_updated":"2022-12-21T19:30:25Z"},{"language":[{"iso":"eng"}],"keyword":["58D15","22E65","26E15","26E20","46E40","46T20","58A05"],"article_type":"original","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"user_id":"178","_id":"34791","status":"public","publication":"Annals of Global Analysis and Geometry","type":"journal_article","doi":"10.1007/s10455-021-09816-y","title":"Manifolds of mappings on Cartesian products","volume":61,"date_created":"2022-12-21T19:24:48Z","author":[{"last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178","first_name":"Helge"},{"last_name":"Schmeding","full_name":"Schmeding, Alexander","first_name":"Alexander"}],"date_updated":"2022-12-21T19:27:09Z","intvolume":"        61","page":"359–398","citation":{"ieee":"H. Glöckner and A. Schmeding, “Manifolds of mappings on Cartesian products,” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, pp. 359–398, 2022, doi: <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>.","chicago":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” <i>Annals of Global Analysis and Geometry</i> 61, no. 2 (2022): 359–398. <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">https://doi.org/10.1007/s10455-021-09816-y</a>.","ama":"Glöckner H, Schmeding A. Manifolds of mappings on Cartesian products. <i>Annals of Global Analysis and Geometry</i>. 2022;61(2):359–398. doi:<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>","apa":"Glöckner, H., &#38; Schmeding, A. (2022). Manifolds of mappings on Cartesian products. <i>Annals of Global Analysis and Geometry</i>, <i>61</i>(2), 359–398. <a href=\"https://doi.org/10.1007/s10455-021-09816-y\">https://doi.org/10.1007/s10455-021-09816-y</a>","short":"H. Glöckner, A. Schmeding, Annals of Global Analysis and Geometry 61 (2022) 359–398.","mla":"Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian Products.” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, 2022, pp. 359–398, doi:<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>.","bibtex":"@article{Glöckner_Schmeding_2022, title={Manifolds of mappings on Cartesian products}, volume={61}, DOI={<a href=\"https://doi.org/10.1007/s10455-021-09816-y\">10.1007/s10455-021-09816-y</a>}, number={2}, journal={Annals of Global Analysis and Geometry}, author={Glöckner, Helge and Schmeding, Alexander}, year={2022}, pages={359–398} }"},"year":"2022","issue":"2","quality_controlled":"1","publication_identifier":{"issn":["0232-704X"]}},{"status":"public","abstract":[{"text":"We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E&times;E is a kR-space.","lang":"eng"}],"type":"journal_article","publication":"Axioms","language":[{"iso":"eng"}],"article_type":"original","user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34796","citation":{"ieee":"H. Glöckner, “Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces,” <i>Axioms</i>, vol. 11, no. 5, 2022, doi: <a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>.","chicago":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i> 11, no. 5 (2022). <a href=\"https://doi.org/10.3390/axioms11050221\">https://doi.org/10.3390/axioms11050221</a>.","ama":"Glöckner H. Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. <i>Axioms</i>. 2022;11(5). doi:<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>","bibtex":"@article{Glöckner_2022, title={Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11}, DOI={<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>}, number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }","short":"H. Glöckner, Axioms 11 (2022).","mla":"Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i>, vol. 11, no. 5, 2022, doi:<a href=\"https://doi.org/10.3390/axioms11050221\">10.3390/axioms11050221</a>.","apa":"Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces. <i>Axioms</i>, <i>11</i>(5). <a href=\"https://doi.org/10.3390/axioms11050221\">https://doi.org/10.3390/axioms11050221</a>"},"intvolume":"        11","year":"2022","issue":"5","quality_controlled":"1","publication_identifier":{"issn":["2075-1680"]},"doi":"10.3390/axioms11050221","title":"Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces","date_created":"2022-12-21T20:02:29Z","author":[{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"}],"volume":11,"date_updated":"2022-12-22T07:31:55Z"},{"user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"external_id":{"arxiv":["2206.11711"]},"_id":"34804","language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2206.11711","status":"public","abstract":[{"lang":"eng","text":"Starting with a finite-dimensional complex Lie algebra, we extend scalars\r\nusing suitable commutative topological algebras. We study Birkhoff\r\ndecompositions for the corresponding loop groups. Some results remain valid for\r\nloop groups with valued in complex Banach-Lie groups."}],"date_created":"2022-12-22T07:42:07Z","author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"}],"date_updated":"2022-12-22T07:44:08Z","title":"Birkhoff decompositions for loop groups with coefficient algebras","citation":{"apa":"Glöckner, H. (2022). Birkhoff decompositions for loop groups with coefficient algebras. In <i>arXiv:2206.11711</i>.","short":"H. Glöckner, ArXiv:2206.11711 (2022).","mla":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” <i>ArXiv:2206.11711</i>, 2022.","bibtex":"@article{Glöckner_2022, title={Birkhoff decompositions for loop groups with coefficient algebras}, journal={arXiv:2206.11711}, author={Glöckner, Helge}, year={2022} }","chicago":"Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient Algebras.” <i>ArXiv:2206.11711</i>, 2022.","ieee":"H. Glöckner, “Birkhoff decompositions for loop groups with coefficient algebras,” <i>arXiv:2206.11711</i>. 2022.","ama":"Glöckner H. Birkhoff decompositions for loop groups with coefficient algebras. <i>arXiv:220611711</i>. Published online 2022."},"year":"2022"},{"title":"Ruelle–Pollicott resonances for manifolds with hyperbolic cusps","publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_created":"2023-01-05T16:23:34Z","year":"2022","issue":"3","keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publication":"Journal of the European Mathematical Society","doi":"10.4171/jems/1103","date_updated":"2023-01-06T08:47:35Z","author":[{"full_name":"Guedes Bonthonneau, Yannick","last_name":"Guedes Bonthonneau","first_name":"Yannick"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias"}],"volume":24,"citation":{"chicago":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i> 24, no. 3 (2022): 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>.","ieee":"Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds with hyperbolic cusps,” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, pp. 851–923, 2022, doi: <a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>.","ama":"Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>. 2022;24(3):851-923. doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>","bibtex":"@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}, volume={24}, DOI={<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>}, number={3}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Guedes Bonthonneau, Yannick and Weich, Tobias}, year={2022}, pages={851–923} }","mla":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 851–923, doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>.","short":"Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.","apa":"Guedes Bonthonneau, Y., &#38; Weich, T. (2022). Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>, <i>24</i>(3), 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>"},"page":"851-923","intvolume":"        24","publication_status":"published","publication_identifier":{"issn":["1435-9855"]},"_id":"35306","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"status":"public","type":"journal_article"},{"date_updated":"2023-01-09T18:07:30Z","author":[{"full_name":"Hanusch, Maximilian","id":"30905","last_name":"Hanusch","first_name":"Maximilian"}],"volume":30,"doi":"10.4310/cag.2022.v30.n1.a2","publication_status":"published","publication_identifier":{"issn":["1019-8385","1944-9992"]},"citation":{"mla":"Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis and Geometry</i>, vol. 30, no. 1, International Press of Boston, 2022, pp. 53–152, doi:<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>.","short":"M. Hanusch, Communications in Analysis and Geometry 30 (2022) 53–152.","bibtex":"@article{Hanusch_2022, title={Regularity of Lie groups}, volume={30}, DOI={<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>}, number={1}, journal={Communications in Analysis and Geometry}, publisher={International Press of Boston}, author={Hanusch, Maximilian}, year={2022}, pages={53–152} }","apa":"Hanusch, M. (2022). Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>, <i>30</i>(1), 53–152. <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>","ieee":"M. Hanusch, “Regularity of Lie groups,” <i>Communications in Analysis and Geometry</i>, vol. 30, no. 1, pp. 53–152, 2022, doi: <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>.","chicago":"Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis and Geometry</i> 30, no. 1 (2022): 53–152. <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>.","ama":"Hanusch M. Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>. 2022;30(1):53-152. doi:<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>"},"intvolume":"        30","page":"53-152","_id":"34817","user_id":"30905","department":[{"_id":"93"}],"article_type":"original","extern":"1","type":"journal_article","status":"public","publisher":"International Press of Boston","date_created":"2022-12-22T09:19:43Z","title":"Regularity of Lie groups","issue":"1","year":"2022","keyword":["regularity of Lie groups"],"language":[{"iso":"eng"}],"publication":"Communications in Analysis and Geometry"},{"status":"public","type":"working_paper","language":[{"iso":"ger"}],"_id":"34856","user_id":"30905","department":[{"_id":"93"}],"year":"2022","citation":{"ama":"Hanusch M. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching","chicago":"Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching, n.d.","ieee":"M. Hanusch, <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.","apa":"Hanusch, M. (n.d.). <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.","short":"M. Hanusch, Analysis 1 und 2 Skript/Buch, https://maximilianhanusch.wixsite.com/my-site/lehre-teaching, n.d.","mla":"Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.","bibtex":"@book{Hanusch, title={Analysis 1 und 2 Skript/Buch}, publisher={https://maximilianhanusch.wixsite.com/my-site/lehre-teaching}, author={Hanusch, Maximilian} }"},"page":"385","publication_status":"draft","title":"Analysis 1 und 2 Skript/Buch","date_updated":"2023-01-09T18:07:00Z","publisher":"https://maximilianhanusch.wixsite.com/my-site/lehre-teaching","date_created":"2022-12-22T17:06:02Z","author":[{"first_name":"Maximilian","last_name":"Hanusch","id":"30905","full_name":"Hanusch, Maximilian"}]},{"publication":"Journal of Physics A: Mathematical and Theoretical","abstract":[{"text":"In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.","lang":"eng"}],"external_id":{"arxiv":["2201.04892"]},"language":[{"iso":"eng"}],"issue":"24","year":"2022","date_created":"2022-05-04T12:23:11Z","publisher":"IOP Publishing Ltd","title":"Semiclassical formulae For Wigner distributions","type":"journal_article","status":"public","department":[{"_id":"623"},{"_id":"548"},{"_id":"10"}],"user_id":"49178","_id":"31057","article_type":"review","article_number":"244007","intvolume":"        55","citation":{"bibtex":"@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For Wigner distributions}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>}, number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd}, author={Barkhofen, Sonja and Schütte, Philipp and Weich, Tobias}, year={2022} }","mla":"Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 24, 244007, IOP Publishing Ltd, 2022, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>.","short":"S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).","apa":"Barkhofen, S., Schütte, P., &#38; Weich, T. (2022). Semiclassical formulae For Wigner distributions. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(24), Article 244007. <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">https://doi.org/10.1088/1751-8121/ac6d2b</a>","ama":"Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(24). doi:<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>","ieee":"S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner distributions,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 24, Art. no. 244007, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>.","chicago":"Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae For Wigner Distributions.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 24 (2022). <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">https://doi.org/10.1088/1751-8121/ac6d2b</a>."},"volume":55,"author":[{"first_name":"Sonja","last_name":"Barkhofen","id":"48188","full_name":"Barkhofen, Sonja"},{"full_name":"Schütte, Philipp","id":"50168","last_name":"Schütte","first_name":"Philipp"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"date_updated":"2024-02-06T20:40:45Z","doi":"10.1088/1751-8121/ac6d2b"},{"status":"public","publication":"Journal of Spectral Theory","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Geometry and Topology","Mathematical Physics","Statistical and Nonlinear Physics"],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"user_id":"49063","_id":"35322","intvolume":"        12","page":"659-681","citation":{"ieee":"K.-U. 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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>"},"year":"2022","issue":"2","publication_identifier":{"issn":["1664-039X"]},"publication_status":"published","doi":"10.4171/jst/414","title":"Poisson transforms for trees of bounded degree","volume":12,"author":[{"full_name":"Bux, Kai-Uwe","last_name":"Bux","first_name":"Kai-Uwe"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"},{"id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"}],"date_created":"2023-01-06T08:49:06Z","date_updated":"2024-02-19T06:28:12Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH"},{"department":[{"_id":"91"}],"user_id":"49063","_id":"51554","language":[{"iso":"eng"}],"publication":"Mathematische Semesterberichte","type":"review","status":"public","volume":69,"author":[{"last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220","first_name":"Joachim"}],"date_created":"2024-02-20T09:49:04Z","date_updated":"2024-02-20T09:52:53Z","doi":"10.1007/s00591-021-00314-7","title":"Ethan D. 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In <i>Mathematische Semesterberichte</i> (Vol. 69, pp. 151–153). <a href=\"https://doi.org/10.1007/s00591-021-00314-7\">https://doi.org/10.1007/s00591-021-00314-7</a>"},"year":"2022"},{"user_id":"15645","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"_id":"35528","language":[{"iso":"eng"}],"type":"journal_article","publication":"Nonlinearity","status":"public","author":[{"full_name":"Lankeit, Johannes","last_name":"Lankeit","first_name":"Johannes"},{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2023-01-09T15:33:38Z","volume":35,"date_updated":"2023-01-20T13:18:15Z","title":"Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary","citation":{"apa":"Lankeit, J., &#38; Winkler, M. (2022). Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary. <i>Nonlinearity</i>, <i>35</i>, 719–749.","mla":"Lankeit, Johannes, and Michael Winkler. “Radial Solutions to a Chemotaxis-Consumption Model Involving Prescribed Signal Concentrations on the Boundary.” <i>Nonlinearity</i>, vol. 35, 2022, pp. 719–49.","bibtex":"@article{Lankeit_Winkler_2022, title={Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary}, volume={35}, journal={Nonlinearity}, author={Lankeit, Johannes and Winkler, Michael}, year={2022}, pages={719–749} }","short":"J. Lankeit, M. Winkler, Nonlinearity 35 (2022) 719–749.","chicago":"Lankeit, Johannes, and Michael Winkler. “Radial Solutions to a Chemotaxis-Consumption Model Involving Prescribed Signal Concentrations on the Boundary.” <i>Nonlinearity</i> 35 (2022): 719–49.","ieee":"J. Lankeit and M. 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Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction. <i>Communications in Mathematical Physics</i>, <i>389</i>, 439–489.","bibtex":"@article{Winkler_2022, title={Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction.}, volume={389}, journal={Communications in Mathematical Physics}, author={Winkler, Michael}, year={2022}, pages={439–489} }","short":"M. Winkler, Communications in Mathematical Physics 389 (2022) 439–489.","mla":"Winkler, Michael. “Reaction-Driven Relaxation in Threee-Dimensional Keller-Segel-Navier-Stokes Interaction.” <i>Communications in Mathematical Physics</i>, vol. 389, 2022, pp. 439–89.","ama":"Winkler M. Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction. <i>Communications in Mathematical Physics</i>. 2022;389:439-489.","ieee":"M. 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