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The growth rate of trajectories of a quadratic differential

Published online by Cambridge University Press:  19 September 2008

Howard Masur
Howard Masur
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60680, USA
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990 , pp. 151 - 176
Copyright
Copyright © Cambridge University Press 1990

References

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