On the orbit function of discrete groups in negative curvature

DOI10.5802/aif.1880zbMath1008.20040OpenAlexW102142704MaRDI QIDQ5956594

Thomas Roblin

Publication date: 21 February 2002

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2002__52_1_145_0

zbMATH Keywords

negative curvaturediscrete groups of isometries of metric spacesorbit functions

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Asymptotic properties of groups (20F69) Orbit growth in dynamical systems (37C35) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85)

Related Items

On horospheric limit sets of Kleinian groups ⋮ Comportement harmonique des densités conformes et frontière de Martin ⋮ Orbital functions and heat kernels of Kleinian groups ⋮ Skinning measures in negative curvature and equidistribution of equidistant submanifolds ⋮ Asymptotic geometry and growth of conjugacy classes of nonpositively curved manifolds ⋮ Convergence and counting in infinite measure ⋮ Poincaré series for non-Riemannian locally symmetric spaces ⋮ Minimal volume entropy for graphs ⋮ Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces ⋮ Conjugacy growth and width of certain branch groups ⋮ Shadow Lemma and nondivergence of the horospheres of a geometrically finite manifold. ⋮ Dimensions of limit sets of Kleinian groups ⋮ Pressure, Poincaré series and box dimension of the boundary ⋮ Quantitative error term in the counting problem on Veech wind-tree models ⋮ On the hyperbolic orbital counting problem in conjugacy classes ⋮ The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group

Cites Work

• Unnamed Item
• Unnamed Item
• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• Topological entropy for geodesic flows
• The density at infinity of a discrete group of hyperbolic motions
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• The limit set of a Fuchsian group
• Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature
• Conformal structure on the boundary and geodesic flow of a \(\text{CAT}(-1)\)-space
• Applications of ergodic theory to the investigation of manifolds of negative curvature