Metric stability for random walks (with applications in renormalization theory)

Details Metric stability for random walks (with applications in renormalization theory) Metric stability for random walks (with applications in renormalization theory)

2005-03-31

arxiv.org/abs/math/0503736v4

Mathematics

Dynamical Systems

58 pages, 5 figures. The authors thank the referee for many valuable suggestions and corrections. To appear in the Proceedings

Scientific paper

Consider deterministic random walks F: I x Z -> I x Z, defined by F(x,n)=(f(x), K(x)+n), where f is an expanding Markov map on the interval I and K: I->Z. We study the universality (stability) of ergodic (for instance, recurrence and transience), geometric and multifractal properties in the class of perturbations of the type G(x,n)=(f_n(x), L(x,n)+n) which are topologically conjugate with F and f_n are expanding maps exponentially close to f when |n| goes to infinity. We give applications of these results in the study of the regularity of conjugacies between (generalized) infinitely renormalizable maps of the interval and the existence of wild attractors for one-dimensional maps.

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