A graph-theoretic bound on the number of independent absolutely continuous invariant measures
type: Item
instance of: scholarly article
title: A graph-theoretic bound on the number of independent absolutely continuous invariant measures
zbMATH Open document ID: 0675.28007
DOI: 10.1016/0022-247X(89)90234-5
author: W. Byers
author: Abraham Boyarsky
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: For piecewise expanding interval maps with slope \(>2\) the authors derive upper bounds on the number of absolutely continuous ergodic invariant measures. These bounds are based on the accessibility graph of the intervals of monotonicity of the transformation. Random compositions of such maps are treated by the same approach. For individual maps a sharper, but not so easily computable bound, based on the Markov diagram of such maps, can be found in section 4 of \textit{F. Hofbauer} [Ergodic Theory Dyn. Syst. 1, 159-178 (1981; Zbl 0474.28007)].
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 4105280
zbMATH Keywords: piecewise expanding interval maps
zbMATH Keywords: upper bounds
zbMATH Keywords: absolutely continuous ergodic invariant measures
zbMATH Keywords: accessibility graph
MaRDI profile type: Publication
cites work: On the Existence of Invariant Measures for Piecewise Monotonic Transformations
cites work: Ergodic Transformations from an Interval Into Itself
cites work: Q4067307
cites work: First return map and invariant measures
cites work: A Result Related to a Theorem by Pianigiani
cites work: The ergodic behaviour of piecewise monotonic transformations
cites work: Q3254327
cites work: Q3943082
cites work: Maximal absolutely continuous invariant measures for piecewise linear Markov transformations
cites work: Invariant Densities for Random Maps of the Interval
cites work: Spectral decomposition for combinations of Markov operators
cites work: Probabilistic Properties of Deterministic Systems
cites work: Stochastic stability in some chaotic dynamical systems
cites work: Irreducibility and primitivity using Markov maps
cites work: Q4149954
full work available at URL: 0022-247x(89)90234-5
OpenAlex ID: W2015426449
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description: scientific article; zbMATH DE number 4105280