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
transformationergodicabsolutely continuous invariant measuresone-dimensional dynamicspiecewise expanding
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
- Unnamed Item
- Absolutely continuous invariant measures for piecewise expanding \(C^ 2\) transformations in \(\mathbb R^N\)
- Higher-dimensional point transformations and asymptotic measures for cellular automata
- A graph-theoretic bound on the number of independent absolutely continuous invariant measures
- First return map and invariant measures
- On the number of invariant measures for higher-dimensional chaotic transformations
- On invariant measures for piecewise $C^2$-transformations of the n-dimensional cube
- 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
- 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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