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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
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
Received: 18.07.2023 Accepted: 25.12.2023
Citation:
Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma
Linking options:
https://www.mathnet.ru/eng/rcd1250
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Abstract page: | 35 | References: | 10 |
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