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Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps

Published online by Cambridge University Press:  30 June 2011

CHINMAYA GUPTA ,
MARK HOLLAND  and
MATTHEW NICOL
CHINMAYA GUPTA
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA (email: ccgupta@math.uh.edu, nicol@math.uh.edu)
MARK HOLLAND
Affiliation:
Math Research Institute, University of Exeter, UK (email: m.p.holland@exeter.ac.uk)
MATTHEW NICOL
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA (email: ccgupta@math.uh.edu, nicol@math.uh.edu)
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Abstract

In this paper we establish extreme value statistics for observations on a class of hyperbolic systems: planar dispersing billiard maps and flows, Lozi maps and Lorenz-like maps. In particular, we show that for time series arising from Hölder observations on these systems which are maximized at generic points the successive maxima of the time series are distributed according to the corresponding extreme value distributions for independent identically distributed processes. These results imply an exponential law for the hitting and return time statistics of these dynamical systems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 5 , October 2011 , pp. 1363 - 1390
Copyright
Copyright © Cambridge University Press 2011

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