Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regular and Chaotic Dynamics, 2024, Volume 29, Issue 1, paper published in the English version journal
DOI: https://doi.org/10.1134/S156035472401009X
(Mi rcd1250)
 

Special Issue: In Honor of Vladimir Belykh and Sergey Gonchenko Guest Editors: Alexey Kazakov, Vladimir Nekorkin, and Dmitry Turaev

Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers

Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma

National Research University Higher School of Economics, ul. Bolshaya Pecherckaya 25/12, 603005 Nizhny Novgorod, Russia
Citations (1)
References:
Abstract: Let $\mathbb{G}_k^{cod 1}(M^n)$, $k\geqslant 1$, be the set of axiom A diffeomorphisms such that the nonwandering set of any $f\in\mathbb{G}_k^{cod 1}(M^n)$ consists of $k$ orientable connected codimension one expanding attractors and contracting repellers where $M^n$ is a closed orientable $n$-manifold, $n\geqslant 3$. We classify the diffeomorphisms from $\mathbb{G}_k^{cod 1}(M^n)$ up to the global conjugacy on nonwandering sets. In addition, we show that any $f\in\mathbb{G}_k^{cod 1}(M^n)$ is $\Omega$-stable and is not structurally stable. One describes the topological structure of a supporting manifold $M^n$.
Keywords: axiom A diffeomorphism, expanding attractor, contracting repeller
Funding agency Grant number
Russian Science Foundation 22-11-00027
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-1101
This work is supported by the Russian Science Foundation under grant 22-11-00027, except Theorem 2 supported by the Laboratory of Dynamical Systems and Applications of the National Research University Higher School of Economics, of the Ministry of Science and Higher Education of the RF, grant ag. 075-15-2022-1101.
Received: 18.07.2023
Accepted: 25.12.2023
Document Type: Article
MSC: 58C30, 37D15
Language: English
Citation: Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma
Citation in format AMSBIB
\Bibitem{GriMedZhu24}
\by Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma
\mathnet{http://mi.mathnet.ru/rcd1250}
\crossref{https://doi.org/10.1134/S156035472401009X}
Linking options:
  • https://www.mathnet.ru/eng/rcd1250
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:35
    References:10
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024