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Asymptotic formulas on flat surfaces. (English) Zbl 1096.37501
Summary: We find asymptotics for the number of cylinders and saddle connections on flat surfaces. These results extend previous results of W. V. Veech [Ann. Math. (2) 148, No. 3, 895–944 (1998; Zbl 0922.22003)]. The authors use an ergodic theorem proved by A. Nevo [Equidistribution in measure preserving actions of semisimple groups, preprint] to find asymptotic quadratic growth rates for the number of closed trajectories on a generic surface.

MSC:
37F30 Quasiconformal methods and Teichm├╝ller theory, etc. (dynamical systems) (MSC2010)
37C35 Orbit growth in dynamical systems
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