Stable ergodicity of dominated systems

2008/12/01 by Martin Andersson, Andersson, Martin
Mathematics · #37D25 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37D25 #msc:37D30

paper · pdf · doi:10.48550/arxiv.0812.0277

22 pages

arxiv created 2008/12/16 · arxiv updated 2009/12/01

Abstract

We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's local stable and unstable manifolds - a notorious problem in the theory of non-uniform hyperbolicity - is often less severe than it appeas to be.

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