The growth rate of trajectories of a quadratic differential

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Abstract

Suppose q is a holomorphic quadratic differential on a compact Riemann surface of genus g 2. Then q defines a metric, flat except at the zeroes. A saddle connection is a geodesic joining two zeroes with no zeroes in its interior. This paper shows the asymptotic growth rate of the number of saddles of length at most T is at most quadratic in T. An application is given to billiards. © 1990, Cambridge University Press. All rights reserved.

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APA

Masur, H. (1990). The growth rate of trajectories of a quadratic differential. Ergodic Theory and Dynamical Systems, 10(1), 151–176. https://doi.org/10.1017/S0143385700005459

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