A survey of recent results on some statistical features of non-uniformly expanding maps
José F. Alves
Discrete & Continuous Dynamical Systems - A 2006, 15(1): 1-20 doi: 10.3934/dcds.2006.15.1
The aim of this paper is to present a survey of recent results on the statistical properties of non-uniformly expanding maps on finite-dimensional Riemannian manifolds. We will mostly focus on the existence of SRB measures, continuity of the SRB measure and its entropy, decay of correlations, and stochastic stability.
keywords: stochastic stability statistical stability decay of correlations SRB measure continuity of entropy.
Non-uniformly expanding dynamics: Stability from a probabilistic viewpoint
José F. Alves
Discrete & Continuous Dynamical Systems - A 2001, 7(2): 363-375 doi: 10.3934/dcds.2001.7.363
We present some recent developments in the theory of smooth dynamical systems exhibiting non-uniformly expanding behavior in the sense of [2]. In particular, we show that these systems have a finite number of SRB measures whose basins cover the whole manifold, and that under some uniform fast approach on the rates of expansion, their dynamics is statistical and stochastically stable.
keywords: statistical stability Non-uniform expansion SRB measure stochastic stability. physical measure
Stochastic behavior of asymptotically expanding maps
José F. Alves
Conference Publications 2001, 2001(Special): 14-21 doi: 10.3934/proc.2001.2001.14
Please refer to Full Text.
keywords: SRB measure Non-uniform expansion stochastic stability. statistical stability physical measure

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