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Regular and Chaotic Dynamics, 2024, Volume 29, Issue 1, paper published in the English version journal
DOI: https://doi.org/10.1134/S1560354724010106
(Mi rcd1251)
 

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
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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
Funding agency Grant number
Russian Science Foundation 22-11-00027
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-1101
The work is supported by the Russian Science Foundation under grant 22-11-00027 except for the results of Section 3 which was supported by the Laboratory of Dynamical Systems and Applications NRU HSE, grant of the Ministry of Science and Higher education of the RF, ag. No. 075-15-2022-1101.
Received: 17.09.2023
Accepted: 10.01.2024
Document Type: Article
MSC: 37B99, 37E30
Language: English
Citation: Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina
Citation in format AMSBIB
\Bibitem{GriPocChi24}
\by Vyacheslav Z. Grines, Olga V. Pochinka, Ekaterina E. Chilina
\mathnet{http://mi.mathnet.ru/rcd1251}
\crossref{https://doi.org/10.1134/S1560354724010106}
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