Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6550

 Google™ Scholar. Others By: Melián, M. Victoria - Pestana, Domingo
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 Title: Geodesic excursions into cusps in finite-volume hyperbolic manifolds Author(s): Melián, M. VictoriaPestana, Domingo Publisher: University of Michigan, Department of Mathematics Issued date: 1993 Citation: Michigan Mathematical Journal, 1993, vol. 40, n. 1, p. 77-93 URI: http://hdl.handle.net/10016/6550 ISSN: 0026-2285 (Print)1945-2365 (Online) DOI: 10.1307/mmj/1029004675 Description: 18 pages, no figures.-- MSC1991 codes: Primary: 53C22; Secondary: 30F40, 58F17.MR#: MR1214056 (94d:53067)Zbl#: Zbl 0793.53052 Abstract: The main goal of the paper is to prove that, for a given non-compact hyperbolic $n$-manifold $M$ of finite volume, $p\in M$, and a number $\alpha$, $0\leq\alpha \leq 1$, the Hausdorff dimension of the set $\{v\in T\sb p\sp 1(M)$: $\lim\sb{t\to\infty} \sup (\text{dist} (\gamma\sb v(t),p)/t)\geq \alpha\}$ is equal to $n(1-\alpha)$, where $\gamma\sb v(t)$ is the geodesic in $M$ emanating from $p$ in the direction of $v$. This generalize a result of [Acta Math. 149, 215-237 (1982)] that, for almost every direction $v$, such a limit is $1/n$, and it is one for just a countable set of directions $v$.\par However we remark that one has to restrict this claim to the class of hyperbolic manifolds with only Abelian parabolic cusps because the authors assume in fact such property for all considered manifolds $M$ [source: Zentralblatt MATH]. Sponsor: Research supported by a grant from CICYT, Ministerio de Educación y Ciencia, Spain. Review: PeerReviewed Publisher version: http://projecteuclid.org/euclid.mmj/1029004675 Keywords: Hausdorff dimensionGeodesicHyperbolic manifoldsParabolic cusps Rights: © The University of Michigan Appears in Collections: DM - GAMA - Artículos de Revistas