A Criterion for Ergodicity of Non-uniformly Hyperbolic Diffeomorphisms
نویسنده
چکیده
A. In this work we exhibit a new criteria for ergodicity of diffeomorphisms involving conditions on Lyapunov exponents and general position of some invariant manifolds. On one hand we derive uniqueness of SRB-measures for transitive surface diffeomorphisms. On the other hand, using recent results on the existence of blenders we give a positive answer, in the C topology, to a conjecture of Pugh-Shub in the context of partially hyperbolic conservative diffeomorphisms with two dimensional center bundle.
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
متن کاملNew Criteria for Ergodicity and Non-uniform Hyperbolicity
In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this criterion in combination with topological devices such as blenders lets us obtain global ergodicity and abundance of non-zero Lyapunov exponents in some context...
متن کاملIntrinsic Ergodicity for Certain Nonhyperbolic Robustly Transitive Systems
We show that a class of robustly transitive diffeomorphisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic and structurally stable, but nevertheless have constant entropy and isomorphic unique measures of maximal entropy.
متن کاملDynamical Coherence of Partially Hyperbolic Diffeomorphisms of Tori Isotopic to Anosov
We show that partially hyperbolic diffeomorphisms of d-dimensional tori isotopic to an Anosov diffeomorphism, where the isotopy is contained in the set of partially hyperbolic diffeomorphisms, are dynamically coherent. As a consequence, we obtain intrinsic ergodicity and measure equivalence for partially hyperbolic diffeomorphisms with one-dimensional center direction that are isotopic to Anoso...
متن کاملLarge deviations in non-uniformly hyperbolic dynamical systems
We prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limit theorems are derived is the analyticity of logarithmic moment generating functions. Among the classes of dynamical systems to which our results apply are piecewise hyperbolic diffeomorphisms, dispers...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008