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Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space
Zeng Lian, New York University, Courant Institute of Mathematical Sciences, NY, and Kening Lu, Brigham Young University, Provo, UT
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Memoirs of the American Mathematical Society
2010; 106 pp; softcover
Volume: 206
ISBN-10: 0-8218-4656-6
ISBN-13: 978-0-8218-4656-8
List Price: US$68
Individual Members: US$40.80
Institutional Members: US$54.40
Order Code: MEMO/206/967
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The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.

Table of Contents

  • Introduction
  • Random dynamical systems and measures of noncompactness
  • Main results
  • Volume function in Banach spaces
  • Gap and distance between closed linear subspaces
  • Lyapunov exponents and oseledets spaces
  • Measurable random invariant complementary subspaces
  • Proof of multiplicative ergodic theorem
  • Stable and unstable manifolds
  • Appendix A. Subadditive ergodic theorem
  • Appendix B. Non-ergodic case
  • Bibliography
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