Extreme Value Distributions for some classes of Non-Uniformly Partially Hyperbolic Dynamical Systems

Details Extreme Value Distributions for some classes of Non-Uniformly Partially Hyperbolic Dynamical Systems Extreme Value Distributions for some classes of Non-Uniformly Partially Hyperbolic Dynamical Systems

2008-09-29

arxiv.org/abs/0809.5017v2

Mathematics

Dynamical Systems

13 pages; modified introduction; added references for introduction; modified stylesheet

Scientific paper

In this note, we obtain verifiable sufficient conditions for the extreme value distribution for a certain class of skew product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the decay of correlations on the product system and the measure of rapidly returning points on the base, lead to a distribution for the maximum of $\Phi(p) = -\log(d(p, p_0))$ that is of the first type. In particular, we establish the Type I distribution for $S^1$ extensions of piecewise $C^2$ uniformly expanding maps of the interval, non-uniformly expanding maps of the interval modeled by a Young Tower, and a skew product extension of a uniformly expanding map with a curve of neutral points.

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