Only rational homology spheres admit Ω(f) to be union of DE attractors

2008/12/06 by Fan Ding, Jianzhong Pan, Ding, Fan +5
Mathematics · #37D45 57R25 57R40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.DS #math.GT #msc:37D45 #msc:57R25 #msc:57R40

paper · pdf · doi:10.48550/arxiv.0812.1260

23 pages, 2 figures

arxiv created 2009/09/05 · arxiv updated 2009/12/01

Abstract

If there exists a diffeomorphism f on a closed, orientable n-manifold M such that the non-wandering set Ω(f) consists of finitely many orientable (±) attractors derived from expanding maps, then M must be a rational homology sphere; moreover all those attractors are of topological dimension n-2. Expanding maps are expanding on (co)homologies.

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