Please use this identifier to cite or link to this item: https://doi.org/10.2140/gt.2014.18.491
Title: Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold
Authors: Bridgeman, M.
Tan, S.P. 
Keywords: Hyperbolic geometry
Identities
Moments
Issue Date: 29-Jan-2014
Citation: Bridgeman, M., Tan, S.P. (2014-01-29). Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold. Geometry and Topology 18 (1) : 491-520. ScholarBank@NUS Repository. https://doi.org/10.2140/gt.2014.18.491
Abstract: In this paper we consider geodesic flow on finite-volume hyperbolic manifolds with non-empty totally geodesic boundary. We analyse the time for the geodesic flow to hit the boundary and derive a formula for the moments of the associated random variable in terms of the orthospectrum. We show that the zeroth and first moments correspond to two cases of known identities for the orthospectrum. We also show that the second moment is given by the average time for the geodesic flow to hit the boundary. We further obtain an explicit formula in terms of the trilogarithm functions for the average time for the geodesic flow to hit the boundary in the surface case.
Source Title: Geometry and Topology
URI: http://scholarbank.nus.edu.sg/handle/10635/103564
ISSN: 14653060
DOI: 10.2140/gt.2014.18.491
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