Abstract:
For flows satisfying Smale's Axiom $A$ on closed manifolds of dimension $n\ge3$ the structure of codimension-one basic sets is described, which are either expanding attractors or contracting repellers. For such nonmixing basic sets special trapping neighbourhoods with boundary components homeomorphic to ${\mathbb S}^{n-2}\times {\mathbb S}^1$ are constructed. This makes it possible to construct a compactification (casing) of the basin of a basic set, which is a locally trivial fibre bundle over a circle, and the extension of the original flow to the casing is a dynamical suspension and a structurally stable flow of attractor-repeller type.
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