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

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 \(M^{n}\).