Stability and limit theorems for sequences of uniformly hyperbolic dynamics

[摘要] In this paper we obtain an almost sure invariance principle for convergent sequences of either Anosov diffeomorphisms or expanding maps on compact Riemannian manifolds and prove an ergodic stability result for such sequences. The sequences of maps need not correspond to typical points of a random dynamical system. The methods in the proof rely on the stability of compositions of hyperbolic dynamical systems and shadowing for sequences of maps. We introduce the notion of sequential conjugacies and prove that these vary in a Lipschitz way with respect to the generating sequences of dynamical systems. As a consequence, we prove stability results for both time-dependent expanding maps and time-depending Anosov diffeomorphisms that complement results in [15]. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Sequential dynamical systems;Sequential conjugacies;Quasi-conjugacies;Limit theorems;Topological stability