Partial Hyperbolicity, Lyapunov Exponents and Stable Ergodicity

نویسندگان

  • D. DOLGOPYAT
  • YA. PESIN
چکیده

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

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Work of Dolgopyat on Partial and Nonuniform Hyperbolicity

The paper is a non-technical survey and is aimed to illustrate Dolgopyat’s profound contributions to smooth ergodic theory. I will discuss some of Dolgopyat’s work on partial hyperbolicity and nonuniform hyperbolicity with emphasis on interaction between the two – the class of dynamical systems with mixed hyperbolicity. On the one hand, this includes uniformly partially hyperbolic diffeomorphis...

متن کامل

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; ...

متن کامل

Lectures on Lyapunov Exponents and Smooth Ergodic Theory

1. Lyapunov Exponents for Differential Equations 2. Abstract Theory of Lyapunov Exponents 3. Regularity of Lyapunov Exponents Associated with Differential Equations 4. Lyapunov Stability Theory 5. The Oseledets Decomposition 6. Dynamical Systems with Nonzero Lyapunov Exponents. Multiplicative Ergodic Theorem 7. Nonuniform Hyperbolicity. Regular Sets 8. Examples of Nonuniformly Hyperbolic System...

متن کامل

New 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 کامل

Lyapunov Exponents and Smooth Ergodic Theory

This book provides a systematic introduction to smooth ergodic theory, including the general theory of Lyapunov exponents, nonuniform hyperbolic theory, stable manifold theory emphasizing absolute continuity of invariant foliations, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The book can be used as a primary textbook for a special topics course on nonuniform hy...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001