Symbolic dynamics for geodesic flows

DOI10.1007/BF02392459zbMath0488.58016MaRDI QIDQ1166180

Caroline Series

Publication date: 1981

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

continued fraction expansionsMarkov shiftAnosov flowadmissible sequencesfundamental group of the surfacegeodesics on the Poincare discsymbolic dynamics for geodesic flows on surfaces of constant negative curvature and finite area

Mathematics Subject Classification ID

Related Items (33)

A decoding problem in dynamics and in number theory ⋮ Backward continued fractions, Hecke groups and invariant measures for transformations of the interval ⋮ Geodesic flows, interval maps, and symbolic dynamics ⋮ Correlations of length spectra for negatively curved manifolds ⋮ Geometrical Markov coding of geodesics on surfaces of constant negative curvature ⋮ Markov families for Anosov flows with an involutive action ⋮ Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds ⋮ Structure of attractors for boundary maps associated to Fuchsian groups ⋮ Combining rational maps and Kleinian groups via orbit equivalence ⋮ Veering branched surfaces, surgeries, and geodesic flows ⋮ STRUCTURAL STABILITY OF MEANDERING-HYPERBOLIC GROUP ACTIONS ⋮ The Sullivan dictionary and Bowen-Series maps ⋮ Singularity of projections of 2-dimensional measures invariant under the geodesic flow ⋮ Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits ⋮ Growth series for the commutator subgroup ⋮ Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces ⋮ Symbolic dynamics and relatively hyperbolic groups. ⋮ The circle problem on surfaces of variable negative curvature ⋮ Symbolic dynamics for three-dimensional flows with positive topological entropy ⋮ The distribution of geodesic excursions out the end of a hyperbolic orbifold and approximation with respect to a Fuchsian group ⋮ Reduction theory of Fuchsian groups ⋮ A note on uniform distribution for primes and closed orbits ⋮ Livsic theorems, maximizing measures and the stable norm ⋮ Finiteness in polygonal billiards on hyperbolic plane ⋮ Local geometry of random geodesics on negatively curved surfaces ⋮ Continued fractions on the Veech surfaces ⋮ Symbolic dynamics for the modular surface and beyond ⋮ Some applications of thermodynamic formalism to manifolds with constant negative curvature ⋮ Finite Partitions for Several Complex Continued Fraction Algorithms ⋮ Asymptotic distribution of closed geodesics ⋮ Lamination languages ⋮ Correlations for pairs of closed geodesics ⋮ On the rate of mixing of Axiom A flows

Cites Work

• Markov maps associated with Fuchsian groups
• Anosov flows with Gibbs measures are also Bernoullian
• The ergodic theory of axiom A flows
• Ergodic theory on compact spaces
• On the metrical transitivity of the geodesics on closed surfaces of constant negative curvature
• Geodesic flows are Bernoullian
• Dynamical systems on homogeneous spaces
• Uniformization, Moduli, and Kleinian Groups†
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