Some variational formulas for Hausdorff dimension, topological entropy, and SRB entropy for hyperbolic dynamical systems

DOI10.1007/BF01050439zbMath0925.58045OpenAlexW2001649831MaRDI QIDQ1379373

Howard Weiss

Publication date: 25 February 1998

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

Full work available at URL: https://doi.org/10.1007/bf01050439

zbMATH Keywords

Hausdorff dimensiontopological entropyhyperbolic dynamical systemvariational formulasAxiom A flowsSRB entropy

Mathematics Subject Classification ID

Entropy in general topology (54C70) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Ergodic theory (37A99) Hausdorff and packing measures (28A78) Dynamical systems with hyperbolic behavior (37D99)

Related Items

Variational analysis for the multifractal spectra of local entropies and Lyapunov exponents, On multifractal rigidity, Multifractal Decomposition of the Entropies Spectrum for Countable Subshifts in Finer Levels Sets, Finer Structure of the Multifractal Spectrum of Local Entropies, Second variational formulae for dimension spectra

Cites Work

• Unnamed Item
• Regularity of topological and metric entropy of hyperbolic flows
• Differentiability and analyticity of topological entropy for Anosov and geodesic flows
• Regularity of measure theoretic entropy for geodesic flows of negative curvature. I
• Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows
• The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces
• Hausdorff dimension for horseshoes
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms