Free energy as a geometric invariant

DOI10.1007/s00220-005-1414-6zbMath1092.53031OpenAlexW2164564790MaRDI QIDQ814910

Howard Weiss, Mark Pollicott

Publication date: 8 February 2006

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-005-1414-6

zbMATH Keywords

geodesicsnegative curvaturemarked length spectrumword length

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35)

Cites Work

• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Riemannian coverings and isospectral manifolds
• The combinatorial structure of cocompact discrete hyperbolic groups
• Markov maps associated with Fuchsian groups
• The length spectra as moduli for compact Riemann surfaces
• Isospectral and non-isometric Riemannian manifolds
• The Lyapunov spectrum for conformal expanding maps and Axiom-A surface diffeomorphisms
• Free energy as a dynamical invariant (or can you hear the shape of a potential?)
• A note on curvature and fundamental group
• Construction of Markov partitions
• Geodesic flows, interval maps, and symbolic dynamics
• Symbolic Dynamics for Hyperbolic Flows
• The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples
• Geometry and spectra of compact Riemann surfaces
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