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Excursion and return times of a geodesic to a subset of a hyperbolic Riemann surface


Author: Andrew Haas
Journal: Proc. Amer. Math. Soc. 141 (2013), 3957-3967
MSC (2010): Primary 30F35; Secondary 32Q45, 37E35, 53D25
DOI: https://doi.org/10.1090/S0002-9939-2013-11767-3
Published electronically: July 30, 2013
MathSciNet review: 3091786
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Abstract: We calculate the asymptotic average rate at which a generic geodesic on a finite area hyperbolic 2-orbifold returns to a subsurface with geodesic boundary. As a consequence we get the average time a generic geodesic spends in such a subsurface. Related results are obtained for excursions into a collar neighborhood of a simple closed geodesic and the associated distribution of excursion depths.


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Additional Information

Andrew Haas
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: haas@math.uconn.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11767-3
Keywords: Hyperbolic surface, Fuchsian group, geodesic flow.
Received by editor(s): February 12, 2011
Received by editor(s) in revised form: January 28, 2012
Published electronically: July 30, 2013
Communicated by: Michael Wolf
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.