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Hölder conjugacies for random dynamical systems

✍ Scribed by Luis Barreira; Claudia Valls

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
331 KB
Volume
223
Category
Article
ISSN
0167-2789

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✦ Synopsis

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 Hölder continuous, with Hölder exponent essentially determined by the ratios of Lyapunov exponents with the same sign. We consider both maps and flows.

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We prove that the semi-conjugacy, obtained by P. Arnoux (1988, Bull. Soc. Math. France 116, 489-500), between an interval exchange map and a translation on the torus is Hölder continuous and we compute the Hölder exponent. This semiconjugacy is a particular case of a space filling curve.

Sternberg theorems for random dynamical
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