A local limit theorem for closed geodesics and homology

Sharp, Richard

doi:10.1090/S0002-9947-04-03534-2

A local limit theorem for closed geodesics and homology
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Trans. Amer. Math. Soc. 356 (2004), 4897-4908 Request permission

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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