Comparison theorems and orbit counting in hyperbolic geometry

DOI10.1090/S0002-9947-98-01756-5zbMath0909.20023OpenAlexW1503851119MaRDI QIDQ4382934

Richard Sharp, Mark Pollicott

Publication date: 24 March 1998

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-01756-5

zbMATH Keywords

generating functionspresentationsgeneratorshyperbolic spacesPoincaré serieshyperbolic groupsweight functionsfinitely presented groupsnegative curvatureKleinian groupsword metricsstrongly Markov groupsorbit counting functionscocompact groups of motions

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Discrete subgroups of Lie groups (22E40) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Discontinuous groups of transformations (57S30) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Variational aspects of group actions in infinite-dimensional spaces (58E40)

Related Items (15)

Central limit theorems for counting measures in coarse negative curvature ⋮ Correlations of length spectra for negatively curved manifolds ⋮ Critical exponents for groups of isometries. ⋮ Counting and boundary limit theorems for representations of Gromov‐hyperbolic groups ⋮ A rigorous version of R. P. Brent's model for the binary Euclidean algorithm ⋮ Cohomologie bornée des surfaces et courants géodésiques ⋮ Typical behaviour along geodesic rays in hyperbolic groups ⋮ Statistics in conjugacy classes in free groups ⋮ Linear actions of free groups ⋮ The Schottky-Klein prime function and counting functions for Fenchel double crosses ⋮ Asymptotic Counting in Conformal Dynamical Systems ⋮ Statistical limit laws for hyperbolic groups ⋮ A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture ⋮ Comparison theorems for closed geodesics on negatively curved surfaces ⋮ Conformal Markov systems, Patterson-Sullivan measure on limit sets and spectral triples

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