2015/11/20 by J. J. Sánchez-Gabites, Sánchez-Gabites, J. J.
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1511.06549
openalex publication_date 2015/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 A(K), it is well known that the inclusion i : K ⊆ 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 ≤ 3.