On the shape of attractors of discrete dynamical systems

J. J. Sánchez-Gabites

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arXiv · 1511.06549

On the shape of attractors of discrete dynamical systems

J. J. Sánchez-Gabites

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Abstract

Let $M$ be a manifold or (more generally) a locally compact, metrizable ANR. If $K$ is an attractor for a flow in $M$, with basin of attraction $\mathcal{A}(K)$, it is well known that the inclusion $i : K \subseteq \mathcal{A}(K)$ is always a shape equivalence. In this paper we investigate to what extent this generalizes to discrete dynamical systems generated by homeomorphisms, proving that it holds if (and only if) $K$ has polyhedral shape. Then we specialize to the case when $M$ is a manifold of dimension $\leq 3$.

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J. J. Sánchez-Gabites. 2015-11-20. On the shape of attractors of discrete dynamical systems. https://arxiv.org/abs/1511.06549

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