Using Ulam's method to calculate entropy and other dynamical invariants

DOI10.1088/0951-7715/12/1/006zbMath0917.58019OpenAlexW2130380694WikidataQ59139601 ScholiaQ59139601MaRDI QIDQ4230954

Gary Froyland

Publication date: 5 August 1999

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/0352d3eafb7e223da5ccb04600eaea216e17e31f

zbMATH Keywords

axiom Aexpanding mapUlam methodmeasure-theoretic entropyAnosov mapLjapunov exponents mapuniformly hyperbolic map

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Entropy and other invariants (28D20) Ergodic theorems, spectral theory, Markov operators (37A30) Rate of convergence, degree of approximation (41A25) Ergodic theory (37A99) Dynamical systems with hyperbolic behavior (37D99)

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Rigorous approximation of diffusion coefficients for expanding maps ⋮ AN EFFICIENT AND ACCURATE METHOD FOR THE ESTIMATION OF ENTROPY AND OTHER DYNAMICAL INVARIANTS FOR PIECEWISE AFFINE CHAOTIC MAPS ⋮ Thirty years of turnstiles and transport ⋮ Tight space-noise tradeoffs in computing the ergodic measure ⋮ Accurate bounds on Lyapunov exponents for expanding maps of the interval ⋮ A piecewise constant method for Frobenius-Perron operators via delta function approximations ⋮ A rigorous computational approach to linear response ⋮ Exponential state estimation, entropy and Lyapunov exponents ⋮ Symbolic images and invariant measures of dynamical systems ⋮ Statistically optimal almost-invariant sets ⋮ Orthonormal expansions of invariant densities for expanding maps ⋮ Finite approximations of Markov operators ⋮ Numerical over-approximation of invariance entropy via finite abstractions

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