Non-uniformly expanding dynamics: Stability from a probabilistic viewpoint

José F. Alves

doi:10.3934/dcds.2001.7.363

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2001, Volume 7, Issue 2: 363-375. Doi: 10.3934/dcds.2001.7.363

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Non-uniformly expanding dynamics: Stability from a probabilistic viewpoint

José F. Alves^1,

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

Revised: October 31, 2000

Published: March 2000

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Abstract

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.

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Mathematics Subject Classification: 37A50, 37C40, 37C75, 37D25, 37H99.

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