On the growth of quotients of Kleinian groups

DOI10.1017/S0143385710000131zbMath1233.37021OpenAlexW2100316780MaRDI QIDQ3012883

Françoise Dal'Bo, Andrea Sambusetti, Jean-Claude Picaud, Marc Peigné

Publication date: 7 July 2011

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

Full work available at URL: https://doi.org/10.1017/s0143385710000131

zbMATH Keywords

quotient groupsKleinian groupspinched negative curvaturecritical exponent of Poincaré seriesorbit counting functions

Mathematics Subject Classification ID

Orbit growth in dynamical systems (37C35) Dynamical systems with hyperbolic orbits and sets (37D05) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (8)

Local limit theorem for symmetric random walks in Gromov-hyperbolic groups ⋮ Growth tightness for groups with contracting elements ⋮ Growth of quotients of groups acting by isometries on Gromov-hyperbolic spaces. ⋮ Patterson-Sullivan measures and growth of relatively hyperbolic groups ⋮ Convergence and counting in infinite measure ⋮ Cogrowth for group actions with strongly contracting elements ⋮ Large deviations for random walks on Gromov-hyperbolic spaces ⋮ Hausdorff dimension of boundaries of relatively hyperbolic groups

Cites Work

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• Poincaré series of finite geometric groups
• Variational principle and Kleinian groups
• Geometrical finiteness with variable negative curvature
• Growth tightness of surface groups
• Growth tightness for word hyperbolic groups.
• On problems related to growth, entropy, and spectrum in group theory
• Asymptotic properties of coverings in negative curvature
• On the growth of nonuniform lattices in pinched negatively curved manifolds
• Limit sets of discrete groups of isometries of exotic hyperbolic spaces
• Ergodicité et équidistribution en courbure négative

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