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Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems

Published online by Cambridge University Press:  17 July 2009

CHINMAYA GUPTA
CHINMAYA GUPTA*
Affiliation:
Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, TX 77204, USA (email: [email protected])
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Abstract

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 Φ(p)=−log(d(p,p0)) that is of the first type. In particular, we establish the type I distribution for S1 extensions of piecewise C2 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 3 , June 2010 , pp. 757 - 771
Copyright
Copyright © Cambridge University Press 2009

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