On the Approximation of Complicated Dynamical Behavior

Abstract

Abstract. We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow to approximate SRB-measures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization of the Frobenius-Perron operator, and two essentially different mathemat-ical concepts are used: the idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from Ergodic Theory concerning the approxima-tion of SRB-measures by invariant measures of stochastically perturbed systems. The efficiency of the methods is illustrated by several numerical examples. Key words. computation of invariant measures, approximation of the Frobenius-Perron oper-ator, computation of SRB-measures, almost invariant set, cyclic behavior AMS subject classifications. 58F11, 65L60, 58F12