Logarithmic laws and unique ergodicity

@article{Chaika2016LogarithmicLA,
  title={Logarithmic laws and unique ergodicity},
  author={Jon Chaika and Rodrigo Trevi{\~n}o},
  journal={arXiv: Dynamical Systems},
  year={2016}
}
We show that Masur's logarithmic law of geodesics in the moduli space of translation surfaces does not imply unique ergodicity of the translation flow, but that a similar law involving the flat systole of a Teichm\"{u}ller geodesic does imply unique ergodicity. It shows that the flat geometry has a better control on ergodic properties of translation flow than hyperbolic geometry. 

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