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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Abstract 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 to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
AbstractList 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 to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
Examines 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.
Author Lu, Kening
Lian, Zeng
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Copyright Copyright 2010 American Mathematical Society
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Keywords Multiplicative Ergodic Theorem
invariant manifolds
infinite dimensional random dynamical systems
Lyapunov exponents
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Notes Volume 206, number 967 (first of 4 numbers).
Includes bibliographical references (p. 105-106)
OCLC 922981778
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Snippet We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are...
Examines the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are...
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SubjectTerms Banach spaces
Ergodic theory
Invariant manifolds
Lyapunov exponents
Random dynamical systems
TableOfContents 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
Title Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space
URI https://www.ams.org/memo/0967/
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Volume 206
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