Vladislav Medvedev


Grines V. Z., Medvedev V. S., Zhuzhoma E. V.
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
Citation: Grines V. Z., Medvedev V. S., Zhuzhoma E. V.,  Classification of Axiom A Diffeomorphisms with Orientable Codimension One Expanding Attractors and Contracting Repellers, Regular and Chaotic Dynamics, 2024, vol. 29, no. 1, pp. 143-155

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