Average of the Intersection Numbers of Pairs of Closed Geodesics in a Surface

Details Average of the Intersection Numbers of Pairs of Closed Geodesics in a Surface Average of the Intersection Numbers of Pairs of Closed Geodesics in a Surface

2012-01-24

arxiv.org/abs/1201.5158v2

Mathematics

Dynamical Systems

6 pages

Scientific paper

For a compact surface with negative curvature X we show that the normalized
average of the intersection numbers of pairs of closed geodesics of X is
asymptotically equal to 1/(2\pi^2(g-1)), where g is the genus of X.

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