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Only rational homology spheres admit Ω(f) to be union of DE attractors
Published online by Cambridge University Press: 04 November 2009
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 is 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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- Copyright © Cambridge University Press 2009