Dimension spectrum of Axiom A diffeomorphisms. II: Gibbs measures

DOI10.1007/BF02187066zbMath0840.58030WikidataQ114018443 ScholiaQ114018443MaRDI QIDQ1906390

Dominique Simpelaere

Publication date: 9 July 1996

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

thermodynamic formalismHausdorff dimensionlarge deviationsfree energy functionGibbs measuresmultifractal

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Fractals (28A80) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Hausdorff and packing measures (28A78) Dynamical aspects of statistical mechanics (37A60)

Related Items (11)

The correlation dimension of the Sierpinski carpet ⋮ The thermodynamic approach to multifractal analysis ⋮ Mean of the singularities of a Gibbs measure ⋮ Uniform approximation problems of expanding Markov maps ⋮ Multifractal spectra and multifractal rigidity for horseshoes ⋮ Diophantine approximation by orbits of expanding Markov maps ⋮ The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples ⋮ Corrigendum to D. Simpelaere: Multifractal decomposition of the Sierpinski carpet. ⋮ A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions ⋮ On the multifractal analysis of Bernoulli convolutions. I: Large-deviation results. ⋮ Multifractal decomposition of the Sierpiński carpet.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The dimension spectrum of Axiom A attractors
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Some relations between dimension and Lyapunov exponents
• Large deviations for multiplicative chaos
• Currents, flows and diffeomorphisms
• Ergodic theory on compact spaces
• Corrigendum to D. Simpelaere: Multifractal decomposition of the Sierpinski carpet.
• The dimension spectrum of some dynamical systems
• Dimension spectrum of Axiom A diffeomorphisms. I: The Bowen-Margulis measure
• The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces
• Hausdorff dimension for horseshoes
• Entropy and large deviation
• Fractal measures and their singularities: The characterization of strange sets
• Dimension, entropy and Lyapunov exponents
• The singularity spectrumf(α) for cookie-cutters
• [https://portal.mardi4nfdi.de/wiki/Publication:4766476 Principe variationnel et syst�mes dynamiques symboliques]
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

This page was built for publication: Dimension spectrum of Axiom A diffeomorphisms. II: Gibbs measures