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Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space
About this Title
Zeng Lian, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 and Kening Lu, Department of Mathematics, Brigham Young University, Provo, Utah 84602
Publication: Memoirs of the American Mathematical Society
Publication Year:
2010; Volume 206, Number 967
ISBNs: 978-0-8218-4656-8 (print); 978-1-4704-0581-6 (online)
DOI: https://doi.org/10.1090/S0065-9266-10-00574-0
Published electronically: January 22, 2010
Keywords: Lyapunov exponents,
Multiplicative Ergodic Theorem,
infinite dimensional random dynamical systems,
invariant manifolds.
MSC: Primary 37H15, 37L55; Secondary 37A30, 47A35, 37D10, 37D25
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
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.- Ludwig Arnold, Trends and open problems in the theory of random dynamical systems, Probability towards 2000 (New York, 1995) Lect. Notes Stat., vol. 128, Springer, New York, 1998, pp. 34–46. MR 1632623, DOI 10.1007/978-1-4612-2224-8_{2}
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