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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A local limit theorem for closed geodesics and homology


Author: Richard Sharp
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4897-4908
MSC (2000): Primary 37C27, 37C30, 37D20, 37D40, 53C22
Published electronically: January 16, 2004
MathSciNet review: 2084404
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Abstract: In this paper, we study the distribution of closed geodesics on a compact negatively curved manifold. We concentrate on geodesics lying in a prescribed homology class and, under certain conditions, obtain a local limit theorem to describe the asymptotic behaviour of the associated counting function as the homology class varies.


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Additional Information

Richard Sharp
Affiliation: Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
Email: sharp@maths.man.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03534-2
PII: S 0002-9947(04)03534-2
Received by editor(s): March 28, 2003
Received by editor(s) in revised form: June 6, 2003
Published electronically: January 16, 2004
Additional Notes: The author was supported by an EPSRC Advanced Research Fellowship
Article copyright: © Copyright 2004 American Mathematical Society