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Intersection numbers of geodesic arcs
Revista Colombiana de Matemáticas
For a compact surface S with constant curvature −κ (for some κ > 0) and genus g ≥ 2, we show that the tails of the distribution of the normalized intersection numbers i(α, β)/l(α)l(β) (where i(α, β) is the intersection number of the closed geodesics α and β and l(·) denotes the geometric length) are estimated by a decreasing exponential function. As a consequence, we find the asymptotic average of the normalized intersection numbers of pairs of closed geodesics on S. In addition, we prove thatdoi:10.15446/recolma.v49n2.60450 fatcat:swwtofk7fnfo5jr3gbjnwosuam