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

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Abstract

Let \(\mathbb{G}_{k}^{cod1}(M^{n})\), \(k\geqslant 1\), be the set of axiom A diffeomorphisms such that the nonwandering set of any \(f\in\mathbb{G}_{k}^{cod1}(M^{n})\) 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 \(\mathbb{G}_{k}^{cod1}(M^{n})\) up to the global conjugacy on nonwandering sets. In addition, we show that any \(f\in\mathbb{G}_{k}^{cod1}(M^{n})\) is \(\Omega\)-stable and is not structurally stable. One describes the topological structure of a supporting manifold \(M^{n}\).

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Funding

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.

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  1. National Research University Higher School of Economics, ul. Bolshaya Pecherckaya 25/12, 603005, Nizhny Novgorod, Russia

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

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  1. Vyacheslav Z. Grines
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  2. Vladislav S. Medvedev
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  3. Evgeny V. Zhuzhoma
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Correspondence to Vladislav S. Medvedev or Evgeny V. Zhuzhoma.

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58C30, 37D15

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Grines, V.Z., Medvedev, V.S. & Zhuzhoma, E.V. Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers. Regul. Chaot. Dyn. 29, 143–155 (2024). https://doi.org/10.1134/S156035472401009X

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  • DOI: https://doi.org/10.1134/S156035472401009X

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