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Article Contents

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

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

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