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.
Author: | Michael Dellnitz, Oliver Junge |
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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) |