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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, New York, NY
Kening Lu :  Brigham Young University, Provo, UT
Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space
eBook ISBN:  978-1-4704-0581-6
Product Code:  MEMO/206/967.E
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
Add to cart
Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space
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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, New York, NY
Kening Lu :  Brigham Young University, Provo, UT
eBook ISBN:  978-1-4704-0581-6
Product Code:  MEMO/206/967.E
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 206; 2010; 106 pp
    MSC: Primary 37; Secondary 47

    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
     
     
    • Chapters
    • 1. Introduction
    • 2. Random Dynamical Systems and Measures of Noncompactness
    • 3. Main Results
    • 4. Volume Function in Banach Spaces
    • 5. Gap and Distance Between Closed Linear Subspaces
    • 6. Lyapunov Exponents and Oseledets Spaces
    • 7. Measurable Random Invariant Complementary Subspaces
    • 8. Proof of Multiplicative Ergodic Theorem
    • 9. Stable and Unstable Manifolds
    • A. Subadditive Ergodic Theorem
    • B. Non-ergodic Case
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 206; 2010; 106 pp
MSC: Primary 37; Secondary 47

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.
  • Chapters
  • 1. Introduction
  • 2. Random Dynamical Systems and Measures of Noncompactness
  • 3. Main Results
  • 4. Volume Function in Banach Spaces
  • 5. Gap and Distance Between Closed Linear Subspaces
  • 6. Lyapunov Exponents and Oseledets Spaces
  • 7. Measurable Random Invariant Complementary Subspaces
  • 8. Proof of Multiplicative Ergodic Theorem
  • 9. Stable and Unstable Manifolds
  • A. Subadditive Ergodic Theorem
  • B. Non-ergodic Case
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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