On the number of invariant measures for higher-dimensional chaotic transformations

DOI10.1007/BF01017979zbMath0746.58048OpenAlexW1994206185MaRDI QIDQ1182255

S. Singh

Publication date: 28 June 1992

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01017979

zbMATH Keywords

ergodic measurechaotic transformationpiecewise \(C^ 2\) transformation

Mathematics Subject Classification ID

Ergodic theory (37A99) Low-dimensional dynamical systems (37E99) Dynamical systems with hyperbolic behavior (37D99) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

Related Items (4)

Invariant measures for random expanding on average Saussol maps ⋮ Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools ⋮ Existence of many ergodic absolutely continuous invariant measures for piecewise-expanding \(C^2\) chaotic transformations in \(\mathbb R^2\) on a fixed number of partitions ⋮ On the number of invariant measures for random expanding maps in higher dimensions

Cites Work

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• Why computers like Lebesgue measure
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• Inadequacy of the bounded variation technique in the ergodic theory of higher-dimensional transformations
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• Uniqueness of Invariant Densities for Certain Random Maps of The Interval
• Probabilistic Properties of Deterministic Systems
• Higher dimensional analogues of the tent maps
• Metric properties of ε-trajectories of dynamical systems with stochastic behaviour
• A Bound on the Number of Invariant Measures
• A Result Related to a Theorem by Pianigiani
• Ergodic Transformations from an Interval Into Itself

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