Multifractal Analysis for Gibbs Ground States

DOI10.1080/1726037X.2006.10698512zbMath1111.37014OpenAlexW1967086245MaRDI QIDQ3429756

Fernando Vericat, Alejandro M. Mesón

Publication date: 20 March 2007

Published in: Journal of Dynamical Systems and Geometric Theories (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/1726037x.2006.10698512

zbMATH Keywords

Gibbs statesmultifractal spectrummaximizing measurezero temperature limitlocal entropiesgeometric and combinatorial approaches

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Topological entropy (37B40) Reflection groups, reflection geometries (51F15) Dimension theory of smooth dynamical systems (37C45)

Cites Work

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• Almost convex groups
• Group completions and limit sets of Kleinian groups
• Free energy as a dynamical invariant (or can you hear the shape of a potential?)
• Dimension theory and Fuchsian groups
• Multifractal analysis of local entropies for expansive homeomorphisms with specification
• Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type
• Geometrical Markov coding of geodesics on surfaces of constant negative curvature
• Gibbs measures at temperature zero
• On a general concept of multifractality: Multifractal spectra for dimensions, entropies, and Lyapunov exponents. Multifractal rigidity

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