Exploring invariant sets and invariant measures
Copyright policy )Exploring invariant sets and invariant measures
We propose a method to explore invariant measures of dynamical systems. The method is based on numerical tools which directly compute invariant sets using a subdivision technique, and invariant measures by a discretization of the Frobenius-Perron operator. Appropriate visualization tools help to analyze the numerical results and to understand important aspects of the underlying dynamics. This will be illustrated for examples provided by the Lorenz system.
- University of Bayreuth Germany
- Zuse Institute Berlin Germany
- University of Freiburg Germany
invariant measures, Lorenz system, Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc., Invariant measures for infinite-dimensional dissipative dynamical systems, Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.), Ergodicity, mixing, rates of mixing, invariant sets, Frobenius-Perron operator
invariant measures, Lorenz system, Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc., Invariant measures for infinite-dimensional dissipative dynamical systems, Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.), Ergodicity, mixing, rates of mixing, invariant sets, Frobenius-Perron operator
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