Abstract
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.
Received by the editors November 27, 1996; accepted for publication (in revised form) February 6, 1998; published electronically February 19, 1999. This research was partially supported by the Deutsche Forschungsgemeinschaft under grant De 448/5-2.
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Dellnitz, M., Junge, O. (1999). On the Approximation of Complicated Dynamical Behavior. In: Hunt, B.R., Li, TY., Kennedy, J.A., Nusse, H.E. (eds) The Theory of Chaotic Attractors. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21830-4_22
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