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Erweiterung im Kontext der COVID-19-Pandemie","publisher":"{Wissenschaftliche Einrichtung Laborschule an der Universität Bielefeld}","date_updated":"2022-05-17T10:28:32Z","author":[{"first_name":"Harry","id":"77972","full_name":"Kullmann, Harry","last_name":"Kullmann"},{"full_name":"Zentarra, Dominik","last_name":"Zentarra","first_name":"Dominik"},{"first_name":"Sabine","full_name":"Geist, Sabine","last_name":"Geist"},{"full_name":"Lütje-Klose, Birgit","last_name":"Lütje-Klose","first_name":"Birgit"},{"full_name":"Siepmann, Christof","last_name":"Siepmann","first_name":"Christof"}],"date_created":"2022-05-03T06:35:49Z"},{"issue":"2","year":"2020","publisher":"Springer Science and Business Media LLC","date_created":"2022-05-17T12:06:06Z","title":"Pollicott-Ruelle Resonant States and Betti Numbers","publication":"Communications in Mathematical Physics","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ne 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>≠</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n</jats:p>"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","intvolume":"       378","page":"917-941","citation":{"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. 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