# Asymptotic formulas on flat surfaces

@article{Eskin2001AsymptoticFO, title={Asymptotic formulas on flat surfaces}, author={A. V. Eskin and Howard A. Masur}, journal={Ergodic Theory and Dynamical Systems}, year={2001}, volume={21}, pages={443 - 478} }

We find asymptotics for the number of cylinders and saddle connections on flat surfaces. These results extend previous results of Veech.

## 143 Citations

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We show that the absolute period foliation of the principal stratum of abelian differentials on a surface of genus at least 3 is ergodic. We also investigate the absolute period foliation of affine…

Deloné property of the holonomy vectors of translation surfaces

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We answer a question posed by Barak Weiss on the uniform discreteness of the set of the holonomy vectors of translation surfaces.

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