On the ergodicity of partially hyperbolic systems
نویسندگان
چکیده
Pugh and Shub [PS3] have conjectured that essential accessibility implies ergodicity, for a C2, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for C1+γ partially hyperbolic systems.
منابع مشابه
Partial Hyperbolicity, Lyapunov Exponents and Stable Ergodicity
We present some results and open problems about stable ergodicity of partially hyperbolic diffeomorphisms with nonzero Lyapunov exponents. The main tool is local ergodicity theory for non-uniformly hyperbolic systems. Dedicated to the great dynamicists David Ruelle and Yakov Sinai on their 65th birthdays
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