Manhattan curves for hyperbolic surfaces with cusps

DOI10.1017/etds.2018.124zbMath1458.37050arXiv1801.09826OpenAlexW2963946019WikidataQ128827045 ScholiaQ128827045MaRDI QIDQ5113036

Lien-Yung Kao

Publication date: 10 June 2020

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.09826

zbMATH Keywords

thermodynamic formalismgroup actionsFuchsian representationsRiemann surfaces with cusps

Mathematics Subject Classification ID

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Teichmüller theory for Riemann surfaces (30F60) Symbolic dynamics (37B10) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Fuchsian and Kleinian groups as dynamical systems (37F32)

Related Items

Pressure metrics for deformation spaces of quasifuchsian groups with parabolics, Pressure metrics and Manhattan curves for Teichmüller spaces of punctured surfaces, Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations

Cites Work

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• On isomorphisms of geometrically finite Möbius groups
• Special flows constructed from countable topological Markov chains
• The Manhattan curve and the correlation of length spectra on hyperbolic surfaces
• Entropy in the cusp and phase transitions for geodesic flows
• Variational principle and Kleinian groups
• Shadow Lemma and nondivergence of the horospheres of a geometrically finite manifold.
• Representation theoretic rigidity in \(PSL(2,\mathbb{R})\)
• Ping-pong groups and closed geodesics in constant negative curvature
• Suspension flows over countable Markov shifts
• Thermodynamic formalism for suspension flows over countable Markov shifts
• Equilibrium states in negative curvature
• Some negatively curved manifolds with cusps, mixing and counting
• Existence of Gibbs measures for countable Markov shifts
• Ergodicité et équidistribution en courbure négative
• Thermodynamic formalism for countable Markov shifts
• Induced topological pressure for countable state Markov shifts
• Hyperbolic manifolds and discrete groups
• Phase transitions for countable Markov shifts
• Gibbs states on the symbolic space over an infinite alphabet
• Marked length rigidity of rank one symmetric spaces and their product