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2014 Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold
Martin Bridgeman, Ser Peow Tan
Geom. Topol. 18(1): 491-520 (2014). DOI: 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.

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Martin Bridgeman. Ser Peow Tan. "Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold." Geom. Topol. 18 (1) 491 - 520, 2014. https://doi.org/10.2140/gt.2014.18.491

Information

Received: 6 March 2013; Revised: 27 June 2013; Accepted: 14 August 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1290.32028
MathSciNet: MR3159167
Digital Object Identifier: 10.2140/gt.2014.18.491

Subjects:
Primary: 32Q45
Secondary: 32G15

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.18 • No. 1 • 2014
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