On the approximation of complicated dynamical behavior

We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow us to approximate Sinai-Ruelle-Bowen (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 mathematical concepts are used: our idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from ergodic theory concerning the approximation of SRB-measures by invariant measures of stochastically perturbed systems. The efficiency of the methods is illustrated by several numerical examples.