Generic properties of invariant measures for continuous piecewise monotonic transformations

DOI10.1007/BF01295288zbMath0669.54021OpenAlexW2065654175MaRDI QIDQ1118850

Franz Hofbauer

Publication date: 1988

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178406

zbMATH Keywords

ergodic measuresstrongly mixing measuresnonatomic measurescontinuous piecewise monotonic transformationdense \(G_{\delta }\)-setsinvariant measures of topologically transitive subsetsmeasures with zero entropy

Mathematics Subject Classification ID

Measure-preserving transformations (28D05)

Related Items

Irregular sets for piecewise monotonic maps, Measures on periodic orbits for continuous transformations on the interval, The growth of periodic orbits with large support, On the generic behavior of the metric entropy, and related quantities, of uniformly continuous maps over Polish metric spaces, Local dimension for piecewise monotonic maps on the interval, Specification on the interval, ENTROPY OF EQUILIBRIUM MEASURES OF CONTINUOUS PIECEWISE MONOTONIC MAPS, Time averages for unpredictable orbits of deterministic systems, Symbolic extensions and continuity properties of the entropy, Omega chaos and the specification property, On the density of periodic measures for piecewise monotonic maps and their coding spaces, The attractor of piecewise expanding maps of the interval, Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems

Cites Work

• Unnamed Item
• Generic properties of invariant measures for simple piecewise monotonic transformations
• Topologically transitive subsets of piecewise monotonic maps, which contain no periodic points
• Ergodic theory on compact spaces
• Generic properties of invariant measures for Axiom A diffeomorphisms