Symbolic dynamics for the modular surface and beyond

DOI10.1090/S0273-0979-06-01115-3zbMath1131.37034OpenAlexW2004702567MaRDI QIDQ3430212

Svetlana Katok, Ilie Ugarcovici

Publication date: 21 March 2007

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-06-01115-3

zbMATH Keywords

modular surface, geodesic flow, continued fractions, Markov partition

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Topological entropy (37B40) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (27)

Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics ⋮ Applications of (a,b)-continued fraction transformations ⋮ Binary quadratic forms as dessins ⋮ Distribution of approximants and geodesic flows ⋮ Symbolic dynamics for one dimensional maps with nonuniform expansion ⋮ Farey maps, Diophantine approximation and Bruhat-Tits tree ⋮ Weighted Riemannian 1-manifolds for classical orthogonal polynomials and their heat kernel ⋮ Veering branched surfaces, surgeries, and geodesic flows ⋮ Geodesic continued fractions ⋮ Pappus Theorem, Schwartz Representations and Anosov Representations ⋮ Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism ⋮ Substitutions, symbolic codings, and discrepancy ⋮ Phase transitions for suspension flows ⋮ Adler and Flatto revisited: cross-sections for geodesic flow on compact surfaces of constant negative curvature ⋮ A new method of coding geodesics on surfaces whose fundamental regions consist of the union of elementary triangles derived from the Farey series ⋮ Symbolic dynamics for three-dimensional flows with positive topological entropy ⋮ Coding of geodesics on some modular surfaces and applications to odd and even continued fractions ⋮ Chaotic Delone sets ⋮ The space of invariant measures for countable Markov shifts ⋮ Uniformly Diophantine numbers in a fixed real quadratic field ⋮ Time change for flows and thermodynamic formalism ⋮ Dynamics of geodesics, and Maass cusp forms ⋮ The symbolic extension theory in topological dynamics ⋮ Finiteness in polygonal billiards on hyperbolic plane ⋮ Symbolic dynamics for non-uniformly hyperbolic systems ⋮ Geodesic flows and the mother of all continued fractions ⋮ Necessary and sufficient conditions for convergence of integer continued fractions

Cites Work

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• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen
• The Teichmüller geodesic flow
• Markov maps associated with Fuchsian groups
• Symbolic dynamics for geodesic flows
• Geometry of surfaces
• Special flows constructed from countable topological Markov chains
• The coding for geodesic flows on a modular surface
• Reduction theory over quadratic imaginary fields
• Coding of closed geodesics after Gauss and Morse
• On the metrical transitivity of the geodesics on closed surfaces of constant negative curvature
• The theta group and the continued fraction expansion with even partial quotients
• Length spectra of the Hecke triangle groups
• Symbolic dynamics for triangle groups
• Reduction theory of Fuchsian groups
• Geodesic flows are Bernoullian
• The isomorphism theorem for Bernoulli flows
• A class of continued fractions associated with certain properly discontinuous groups
• Distribution of closed geodesics on the modular surface and quadratic irrationals
• The Modular Surface and Continued Fractions
• Cross section map for the geodesic flow on the modular surface
• The thermodynamic formalism approach to Selberg’s zeta function for 𝑃𝑆𝐿(2,𝐙)
• The backward continued fraction map and geodesic flow
• Geometrical Markov coding of geodesics on surfaces of constant negative curvature
• Geodesics on modular surfaces and continued fractions
• Geodesic flows, interval maps, and symbolic dynamics
• Hecke groups and continued fractions
• On a $\zeta$ function related to the continued fraction transformation
• Symbolic dynamics and Markov partitions
• On a measure with maximal entropy for the special flow on a local perturbation of a countable topological Bernoulli scheme
• ENTROPY, A COMPLETE METRIC INVARIANT FOR AUTOMORPHISMS OF THE TORUS
• The Equidistribution of Closed Geodesics
• A Metrically Transitive Group Defined by the Modular Groups
• Fractions
• Cutting sequences for geodesic flow on the modular surface and continued fractions

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