Logarithmic laws and unique ergodicity
arXiv:1603.00076 · doi:10.3934/jmd.2017022
Abstract
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 Teichmüller geodesic does imply unique ergodicity. It shows that the flat geometry has a better control on ergodic properties of translation flow than hyperbolic geometry.
24 pages