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Dynamical borel-cantelli lemma for hyperbolic spaces

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Abstract

We prove that almost every (resp. almost no) geodesic rays in a finite volume hyperbolic manifold of real dimensionn intersects for arbitrary large timest a decreasing family of balls of radiusr t, provided the integral ∫ ∞0 r nt −1 dt diverges (resp. converges).

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  1. U.M.P.A., 46, Allée d’Italie, F-69364, Lyon Cedex 07, France

    François Maucourant

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  1. François Maucourant
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Maucourant, F. Dynamical borel-cantelli lemma for hyperbolic spaces. Isr. J. Math. 152, 143–155 (2006). https://doi.org/10.1007/BF02771980

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  • DOI: https://doi.org/10.1007/BF02771980

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