Diophantine approximations for translation surfaces and planar resonant sets

@article{Marchese2015DiophantineAF,
  title={Diophantine approximations for translation surfaces and planar resonant sets},
  author={L. Marchese and Rodrigo Trevi{\~n}o and Steffen Weil},
  journal={arXiv: Dynamical Systems},
  year={2015}
}
  • L. Marchese, Rodrigo Treviño, Steffen Weil
  • Published 2015
  • Mathematics
  • arXiv: Dynamical Systems
  • We consider Teichm\"uller geodesics in strata of translation surfaces. We prove lower and upper bounds for the Hausdorff dimension of the set of parameters generating a geodesic bounded in some compact part of the stratum. Then we compute the dimension of those parameters generating geodesics that make excursions to infinity at a prescribed rate. Finally we compute the dimension of the set of directions in a rational billiard having fast recurrence, which corresponds to a dynamical version of a… CONTINUE READING
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