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Smooth Ergodic Theory of Random Dynamical Systems

  • Book
  • © 1995

Overview

Authors:
  1. Pei-Dong Liu
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    You can also search for this author in PubMed   Google Scholar

  2. Min Qian
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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1606)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Preliminaries

    • Pei-Dong Liu, Min Qian
    Pages 1-21

  3. Entropy and Lyapunov exponents of random diffeomorphisms

    • Pei-Dong Liu, Min Qian
    Pages 22-44

  4. Estimation of entropy from above through Lyapunov exponents

    • Pei-Dong Liu, Min Qian
    Pages 45-54

  5. Stable invariant manifolds of random diffeomorphisms

    • Pei-Dong Liu, Min Qian
    Pages 55-90

  6. Estimation of entropy from below through Lyapunov exponents

    • Pei-Dong Liu, Min Qian
    Pages 91-108

  7. Stochastic flows of diffeomorphisms

    • Pei-Dong Liu, Min Qian
    Pages 109-127

  8. Characterization of measures satisfying entropy formula

    • Pei-Dong Liu, Min Qian
    Pages 128-181

  9. Random perturbations of hyperbolic attractors

    • Pei-Dong Liu, Min Qian
    Pages 182-206

  10. Back Matter

    Pages 207-221
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Keywords

About this book

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

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