Rare events, exponential hitting times and extremal indices via spectral perturbation†

Abstract

We discuss how an eigenvalue perturbation formula for transfer operators of dynamical systems is related to exponential hitting time distributions and extreme value theory for processes generated by chaotic dynamical systems. We also list a number of piecewise expanding systems to which this general theory applies and discuss the prospects to apply this theory to some classes of piecewise hyperbolic systems. †In memory of Jaroslav Stark.