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Random dynamical systems: a review

โœ Scribed by Rabi Bhattacharya; Mukul Majumdar

Publisher
Springer
Year
2003
Tongue
English
Weight
256 KB
Volume
23
Category
Article
ISSN
0938-2259

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## Abstract In this paper, we prove the smooth conjugacy theorems of Sternberg type for random dynamical systems based on their Lyapunov exponents. We also present a stable and unstable manifold theorem with tempered estimates that are used to construct conjugacy. ยฉ 2005 Wiley Periodicals, Inc.

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We establish a Grobman-Hartman theorem for perturbations of random dynamical systems, along orbits with nonzero Lyapunov exponents. The main novelty is that the conjugacies are always Hรถlder continuous, with Hรถlder exponent essentially determined by the ratios of Lyapunov exponents with the same sig