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Special Issue: In Honor of Vladimir Belykh and Sergey Gonchenko Guest Editors: Alexey Kazakov, Vladimir Nekorkin, and Dmitry Turaev
On Homeomorphisms of Three-Dimensional Manifolds with Pseudo-Anosov Attractors and Repellers
Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina International Laboratory of Dynamical Systems and Applications, HSE University,
ul. Bolshaya Pecherckaya 25/12, 603155 Nizhny Novgorod, Russia
Abstract:
The present paper is devoted to a study of orientation-preserving homeomorphisms
on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface
attractors and repellers. The main results of the paper relate to a class of homeomorphisms
for which the restriction of the map to a connected component of the non-wandering set
is topologically conjugate to an orientation-preserving pseudo-Anosov homeomorphism. The
ambient $\Omega$-conjugacy of a homeomorphism from the class with a locally direct product of a
pseudo-Anosov homeomorphism and a rough transformation of the circle is proved. In addition,
we prove that the centralizer of a pseudo-Anosov homeomorphisms consists of only pseudo-
Anosov and periodic maps.
Keywords:
pseudo-Anosov homeomorphism, two-dimensional attractor
Received: 17.09.2023 Accepted: 10.01.2024
Citation:
Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina
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https://www.mathnet.ru/eng/rcd1251
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Abstract page: | 41 | References: | 18 |
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