Intrinsic ergodicity of affine maps in \([0,1]^ d\)

DOI10.1007/BF01300614zbMath0886.58024OpenAlexW2123152740MaRDI QIDQ1366660

Jérôme Buzzi

Publication date: 18 September 1997

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

Full work available at URL: https://eudml.org/doc/178783

zbMATH Keywords

measures of maximal entropyMarkov diagrams

Mathematics Subject Classification ID

Ergodic theory (37A99) Low-dimensional dynamical systems (37E99)

Related Items

Intrinsic ergodicity of smooth interval maps, Conditioning problems for invariant sets of expanding piecewise affine mappings: application to loss of ergodicity in globally coupled maps, Asymptotich-expansiveness rate ofC^∞maps, Symbolic dynamics for one dimensional maps with nonuniform expansion, The shrinking target problem for matrix transformations of tori: revisiting the standard problem, Absolutely continuous invariant measures for multidimensional expanding maps, Specification and towers in shift spaces, Subshifts of quasi-finite type, Dynamics and entropy in the Zhang model of self-organized criticality, Breaking of ergodicity in expanding systems of globally coupled piecewise affine circle maps, Good Banach spaces for piecewise hyperbolic maps via interpolation, Markov extensions for multi-dimensional dynamical systems, ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR GENERIC MULTI-DIMENSIONAL PIECEWISE AFFINE EXPANDING MAPS, Maximal entropy measures for piecewise affine surface homeomorphisms, EXPONENTIAL INEQUALITIES AND FUNCTIONAL ESTIMATIONS FOR WEAK DEPENDENT DATA: APPLICATIONS TO DYNAMICAL SYSTEMS, Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles, Decay of correlations for piecewise invertible maps in higher dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Absolutely continuous invariant measures for piecewise expanding \(C^ 2\) transformations in \(\mathbb R^N\)
• Isomorphisms of \(\beta\)-automorphisms to Markov automorphisms
• Lifting measures to Markov extensions
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki
• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Intrinsic ergodicity of smooth interval maps
• Ergodic properties of nonnegative matrices. I
• On the uniqueness of equilibrium states for piecewise monotone mappings
• Exponents, attractors and Hopf decompositions for interval maps
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• GEOMETRIC ERGODICITY IN DENUMERABLE MARKOV CHAINS
• The entropies of topological Markov shifts and a related class of algebraic integers
• The structure of piecewise monotonic transformations
• Some properties of absolutely continuous invariant measures on an interval
• Some systems with unique equilibrium states
• On Rohlin's formula for entropy
• Entropy for Group Endomorphisms and Homogeneous Spaces
• Intrinsically ergodic systems
• \(\beta\)-shifts have unique maximal measure
• Equilibrium states for \(\beta\)-transformations and related transformations