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Computations in dynamical systems via random perturbations

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  • I consider discretized random perturbations of hyperbolic dynamical systems and prove that when perturbation parameter tends to zero invariant measures of corresponding Markov chains converge to the Sinai-Bowen-Ruelle measure of the dynamical system. This provides a robust method for computations of such measures and for visualizations of some hyperbolic attractors by modeling randomly perturbed dynamical systems on a computer. Similar results are true for discretized random perturbations of maps of the interval satisfying the Misiurewicz condition considered in [KK].
    Mathematics Subject Classification: Primary: 58F15; Secondary: 34F05, 65L99.


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