# American Institue of Mathematical Sciences

2001, 7(2): 363-375. doi: 10.3934/dcds.2001.7.363

## Non-uniformly expanding dynamics: Stability from a probabilistic viewpoint

 1 Department of Mathematics, University of Porto, 4099-002 Porto, Portugal

Revised  November 2000 Published  January 2001

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.
Citation: José F. Alves. Non-uniformly expanding dynamics: Stability from a probabilistic viewpoint. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 363-375. doi: 10.3934/dcds.2001.7.363
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