A graph-theoretic bound on the number of independent absolutely continuous invariant measures

DOI10.1016/0022-247X(89)90234-5zbMath0675.28007OpenAlexW2015426449MaRDI QIDQ1122019

W. Byers, Boyarski, Abraham

Publication date: 1989

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(89)90234-5

zbMATH Keywords

upper boundsabsolutely continuous ergodic invariant measuresaccessibility graphpiecewise expanding interval maps

Mathematics Subject Classification ID

Measure-preserving transformations (28D05)

Related Items (3)

Maximal absolutely continuous invariant measures for piecewise linear Markov transformations ⋮ On the number of invariant measures for higher-dimensional chaotic transformations ⋮ 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

Cites Work

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• Spectral decomposition for combinations of Markov operators
• First return map and invariant measures
• Irreducibility and primitivity using Markov maps
• Stochastic stability in some chaotic dynamical systems
• Invariant Densities for Random Maps of the Interval
• Maximal absolutely continuous invariant measures for piecewise linear Markov transformations
• Probabilistic Properties of Deterministic Systems
• A Result Related to a Theorem by Pianigiani
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• Ergodic Transformations from an Interval Into Itself
• The ergodic behaviour of piecewise monotonic transformations

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