Fast mixing for attractors with a mostly contracting central direction

Abstract

Link to this article: http://journals.cambridge.org/abstract_S0143385703000294How to cite this article: AUGUSTO ARMANDO DE CASTRO JÚNIOR (2004). Fast mixing for attractors with a mostly contracting central direction.Abstract. Bonatti and Viana introduced a robust (non-empty interior) class of partially hyperbolic attractors of C 2 -diffeomorphisms on a compact manifold, for which they construct Sinai-Ruelle-Bowen measures. For some such robust examples, we prove the exponential decay of correlations and the central limit theorem, in the space of Hölder continuous functions. For the proof, we adapt the techniques (backward inducing, redundancy elimination algorithm) we have previously developed.Downloaded

Almost sure rates of mixing for partially hyperbolic attractors

“…As in the case of deterministic dynamical systems, some knowledge on the correlation decay rate of the underlying system is required to obtain probabilistic limit laws for random dynamical systems. However, despite the pioneering work of [18,26], which was followed by [46], and the recent progress made in [15] on almost sure correlation decay rates for random endomorphisms, there are no general tools on the almost sure correlation decay rates for random dynamical systems where the constituent maps are partially hyperbolic diffeomorphisms.…”

Shadowing by non-uniformly hyperbolic periodic points and uniform hyperbolicity

“…Due to lemma 2.7 in [4] (see also proposition 2.23 in [2]), n is also a √ ς -hyperbolic time for x. In particular, this implies that…”

“…Due to proposition 2.23 in [2], n is also a √ ς -hyperbolic time for x. More precisely, this means that…”

Exponential mixing for heterochaos baker maps and the Dyck system

“…Young's method [35,36] of deducing nice statistical properties using towers with fast decaying tails has been successfully implemented for some partially hyperbolic systems, e.g., [3,8,9,13] to deduce exponential decay of correlations. With more functional analytic methods, exponential decay of correlations was proved for certain partially hyperbolic diffeomorphisms [10], and for certain piecewise partially hyperbolic endomorphisms [4].…”