Stable ergodicity of dominated systems
نویسنده
چکیده
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.
منابع مشابه
Denseness of ergodicity for a class of partially hyperbolic volume-preserving flows
Let P be the set of C1 partially hyperbolic volume-preserving flows with one dimensional central direction endowed with the C1flow topology. We prove that any X ∈ P can be approximated by an ergodic C2 volume-preserving flow. As a consequence ergodicity is dense in P. MSC 2000: primary 37D30, 37D25; secondary 37A99. keywords: Dominated splitting; Partial hyperbolicity; Volume-preserving flows; ...
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تاریخ انتشار 2008