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

DOI10.1007/BF02765534zbMath0918.58042OpenAlexW2084704691MaRDI QIDQ1285118

Harald Proppe, Kourosh Adl-Zarabi

Publication date: 4 August 1999

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

Full work available at URL: https://doi.org/10.1007/bf02765534

zbMATH Keywords

transformationergodicabsolutely continuous invariant measuresone-dimensional dynamicspiecewise expanding

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical aspects of measure-preserving transformations (37A05) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Cites Work

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• A Result Related to a Theorem by Pianigiani
• Differential Topology
• Ergodic Transformations from an Interval Into Itself
• Absolutely continuous invariant measures for piecewise expanding C² transformations in Rⁿ on domains with cusps on the boundaries

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