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

Abstract

AbstractIn 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.