The infinite word problem and limit sets in Fuchsian groups

DOI10.1017/S0143385700001280zbMath0483.30029MaRDI QIDQ3941655

Caroline Series

Publication date: 1981

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

zbMATH Keywords

geodesiclimit setsGibbs measurestesselationfinitely generated Fuchsian groupfundamental polygonDehn's solutionformally sequences of generatorsinfinite word problem

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (26)

Diophantine approximation on hyperbolic Riemann surfaces ⋮ Geodesic flows, interval maps, and symbolic dynamics ⋮ Undecidability and chaos in word-coded symbolic dynamics ⋮ A symmetric Markov coding and the ergodic theorem for actions of Fuchsian groups ⋮ Algebraic linearity for an automorphism of a surface group ⋮ Conformal fractals for normal subgroups of free groups ⋮ Convergence of spherical averages for actions of Fuchsian groups ⋮ Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve ⋮ Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits ⋮ Cohomologie bornée des surfaces et courants géodésiques ⋮ Harmonic functions on infinite graphs ⋮ A pointwise ergodic theorem for Fuchsian groups ⋮ Renewal theory for random walks on surface groups ⋮ Coding of geodesics and Lorenz-like templates for some geodesic flows ⋮ Comparison theorems and orbit counting in hyperbolic geometry ⋮ Schottky groups and counting. ⋮ Recurrence and pressure for group extensions ⋮ Representation theoretic rigidity in \(PSL(2,\mathbb{R})\) ⋮ Asymptotic Counting in Conformal Dynamical Systems ⋮ A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture ⋮ The conformal measures of a normal subgroup of a cocompact Fuchsian group ⋮ Martin boundaries of random walks on Fuchsian groups ⋮ New dynamical invariants on hyperbolic manifolds ⋮ Some applications of thermodynamic formalism to manifolds with constant negative curvature ⋮ Asymptotic distribution of closed geodesics ⋮ Correlations for pairs of closed geodesics

Cites Work

• Group completions and limit sets of Kleinian groups
• Markov maps associated with Fuchsian groups
• On Poincaré's theorem for fundamental polygons
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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