Metric stability for random walks (with applications in renormalization theory)
Abstract
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.
Cite
@article{arxiv.math/0503736,
title = {Metric stability for random walks (with applications in renormalization theory)},
author = {Carlos G. Moreira and Daniel Smania},
journal= {arXiv preprint arXiv:math/0503736},
year = {2012}
}
Comments
58 pages, 5 figures. The authors thank the referee for many valuable suggestions and corrections. To appear in the Proceedings of the conference Frontiers in Complex Dynamics (Celebrating John Milnor's 80th. birthday)