1 Multiplicities in the simple length spectrum


Let Σg,n be a surface of genus g with n boundary components together with a hyperbolic structure σ, that is a metric of constant curvature −1, of finite area such that the boundary curves are totally geodesic. Define the full length spectrum to be the collection of all lengths of primitive closed geodesics on the surface counted with multiplicities and the simple length spectrum to be the set of lengths of all simple closed geodesics counted with multiplicities. As the hyperbolic structure varies, the length spectrum changes. In his thesis Margulis gave a solution to counting problem for the full length spectrum for a closed surface. The number of primitive geodesics of length less than L is e/L,

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@inproceedings{Rivin20071MI, title={1 Multiplicities in the simple length spectrum}, author={Igor Rivin}, year={2007} }