Continuity of the measure of maximal entropy for unimodal maps on the interval

DOI10.1007/BF02972823zbMath1207.37026OpenAlexW2167599788MaRDI QIDQ1431463

Peter Raith

Publication date: 9 June 2004

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02972823

zbMATH Keywords

perturbationtopological entropyunimodal mapmeasure of maximal entropyMarkov diagram

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamical systems involving maps of the interval (37E05)

Related Items (5)

Singular limits of absolutely continuous invariant measures for families of transitive maps ⋮ Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps ⋮ Entropy formula and continuity of entropy for piecewise expanding maps ⋮ Diabolical entropy ⋮ Uniqueness and continuity of equilibrium states for DA-diffeomorphisms

Cites Work

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• Piecewise invertible dynamical systems
• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. II
• Continuity of the Hausdorff dimension for piecewise monotonic maps
• Stability of the topological pressure for piecewise monotonic maps under \(C^1\)-perturbations
• Discontinuities of the pressure for piecewise monotonic interval maps
• Maximal measures for simple piecewise monotonic transformations
• Jumps of entropy in one dimension
• Entropy of piecewise monotone mappings
• Stability of the maximal measure for piecewise monotonic interval maps

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