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Counting orbit points in coverings of negatively curved manifolds and Hausdorff dimension of cusp excursions

Published online by Cambridge University Press:  04 May 2004

SA'AR HERSONSKY  and
FRÉDÉRIC PAULIN
SA'AR HERSONSKY
Affiliation:
Department of Mathematics, Ben Gurion University, Beer-Sheva, Israel (e-mail: saarh@math.bgu.ac.il)
FRÉDÉRIC PAULIN
Affiliation:
Département de Mathématique et Applications, UMR 8553 CNRS, École Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France (e-mail: Frederic.Paulin@ens.fr)
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Abstract

We study the growth of fibers of coverings of pinched negatively curved Riemannian manifolds. The applications include counting estimates for horoballs in the universal cover of geometrically finite manifolds with cusps. Continuing our work on diophantine approximation in negatively curved manifolds started in an earlier paper (Math. Zeit.241 (2002), 181–226), we prove a Khintchine–Sullivan-type theorem giving the Hausdorff measure of the geodesic lines starting from a cusp that are well approximated by the cusp returning ones.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 3 , June 2004 , pp. 803 - 824
Copyright
2004 Cambridge University Press

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