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On the Approximation of Complicated Dynamical Behavior

Please always quote using this URN: urn:nbn:de:0297-zib-2456
  • We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow to approximate SBR-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: the idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from Ergodic Theory concerning the approximation of SBR-measures by invariant measures of stochastically perturbed systems. The efficiency of the methods is illustrated by several numerical examples.

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Metadaten
Author:Michael Dellnitz, Oliver Junge
Document Type:ZIB-Report
Date of first Publication:1996/11/19
Series (Serial Number):ZIB-Report (SC-96-35)
ZIB-Reportnumber:SC-96-35
Published in:Appeared in: SIAM Journal on Numerical Analysis 36 (2) 491-515 (1999)
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