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The Hausdorff dimension of bounded geodesics on geometrically finite manifolds

Published online by Cambridge University Press:  17 April 2001

B. STRATMANN
B. STRATMANN
Affiliation:
Mathematisches Institut der Universität Göttingen, SFB 170, Bunsenstr. 3-5, 37073 Göttingen, Germany (e-mail: [email protected])
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Abstract

In this paper we study the set of bounded geodesics on a general, geometrically finite $(N+1)$-manifold of constant negative curvature. We obtain the result that the Hausdorff dimension of this set is equal to $2 \delta$, where $\delta$ denotes the exponent of convergence of the associated Kleinian group. The proof of this shows, in particular, that if the group has parabolic elements, then the set of limit points which are badly approximable with respect to the parabolic fixed points has Hausdorff dimension equal to $\delta$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 1 , February 1997 , pp. 227 - 246
Copyright
1997 Cambridge University Press

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