Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space

We 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. We prove a multiplicative ergodic theorem. Then, we use this theorem...

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Hlavní autoři: Lian, Zeng, Lu, Kening
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2010
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Banach spaces
Ergodic theory
Invariant manifolds
Lyapunov exponents
Random dynamical systems
Multiplicative Ergodic Theorem
invariant manifolds
infinite dimensional random dynamical systems
Lyapunov exponents
ISBN:0821846566, 9780821846568
ISSN:0065-9266, 1947-6221
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Obsah:
  • 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 -- Subadditive Ergodic Theorem -- Non-ergodic Case
  • Intro -- Contents -- Abstract -- Chapter 1. Introduction -- Acknowledgement -- Chapter 2. Random Dynamical Systems and Measures of Noncompactness -- Chapter 3. Main Results -- Chapter 4. Volume Function in Banach Spaces -- Chapter 5. Gap and Distance Between Closed Linear Subspaces -- Chapter 6. Lyapunov Exponents and Oseledets Spaces -- Chapter 7. Measurable Random Invariant Complementary Subspaces -- Chapter 8. Proof of Multiplicative Ergodic Theorem -- Chapter 9. Stable and Unstable Manifolds -- Appendix A. Subadditive Ergodic Theorem -- Appendix B. Non-ergodic Case -- Bibliography