Computations in dynamical systems via random perturbations

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Viscosity solutions and uniqueness for systems of inhomogeneous balance laws

October 1997, 3(4): 457-476. doi: 10.3934/dcds.1997.3.457

Computations in dynamical systems via random perturbations

1.	Institute of Mathematics, Hebrew University, Jerusalem 91904

Received March 1997 Published July 1997

Abstract
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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].

Keywords: Dynamical systems, random perturbations., discretizations.

Mathematics Subject Classification: Primary: 58F15; Secondary: 34F05, 65L9.

Citation: Yuri Kifer. Computations in dynamical systems via random perturbations. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 457-476. doi: 10.3934/dcds.1997.3.457

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