Minimal Cantor Systems and Unimodal Maps

DOI10.1080/1023619021000047743zbMath1026.37003OpenAlexW2121516478WikidataQ59184886 ScholiaQ59184886MaRDI QIDQ4408577

Henk Bruin

Publication date: 8 December 2003

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/1023619021000047743

zbMATH Keywords

unimodal mapsBratelli diagramsminimal Cantor setVershik adic transformations

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Symbolic dynamics (37B10)

Related Items (9)

Invariant measures for interval maps without Lyapunov exponents ⋮ Choquet simplices as spaces of invariant probability measures on post-critical sets ⋮ Topological orbit equivalence classes and numeration scales of logistic maps ⋮ Products and decompositions of adding machines ⋮ The complexity of Fibonacci-like kneading sequences ⋮ Invariant measures of minimal post-critical sets of logistic maps ⋮ Natural equilibrium states for multimodal maps ⋮ Existence of unique SRB-measures is typical for real unicritical polynomial families ⋮ Transience in dynamical systems

Cites Work

• Topological entropy of the transformation \(x\mapsto ax(1-x)\)
• A characterization of substitutive sequences using return words
• Wild Cantor attractors exist
• Substitutional dynamical systems, Bratteli diagrams and dimension groups
• Some properties of absolutely continuous invariant measures on an interval
• COMBINATORICS OF THE KNEADING MAP
• Topological conditions for the existence of absorbing Cantor sets
• Linearly recurrent subshifts have a finite number of non-periodic subshift factors
• Dynamiques associees a une echelle de numeration
• Rank and symbolic complexity

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