Lyapunov Exponents and Invariant Manifold 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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| Format: | Others |
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BYU ScholarsArchive
2008
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| Online Access: | https://scholarsarchive.byu.edu/etd/1517 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2516&context=etd |
| Summary: | 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. |
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