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Конференция «Hyperbolic Dynamics and Structural Stability», посвященная 85-летию Д. В. Аносова
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Birkhoff sections and orbit spaces of Anosov flows Theo Marty Max Planck Institute for Mathematics, Bonn |
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Аннотация: An Anosov flow in dimension 3 can be studied using transverse surfaces called Birkhoff sections. We consider the sign of the boundary components of a Birkhoff section to deduce topological properties of the flow. Theorem. [Masayuki Asaoka [1], T.M [2], Christian Bonatti 2021'] An Anosov flow on a closed oriented 3-manifold admits a positive Birkhoff section if and only if it is I will discuss one proof of the theorem together with some relations with Fried-Goodman surgeries and Reeb flows. Notice that this theorem admits two other independent proofs found by Masayuki Asaoka [1] and Christian Bonatti. [1] Masayuki Asaoka, Goodman-Fried surgery, Birkhoff section, and R-covered Anosov flows, arXiv 2108.08215, 2021 [2] Théo Marty, Flots d'Anosov et sections de Birkhoff, thesis manuscript, 2021 Язык доклада: английский |