Logarithmic laws and unique ergodicity
Jon Chaika Rodrigo Treviño
Journal of Modern Dynamics 2017, 11(1): 563-588 doi: 10.3934/jmd.2017022

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.

keywords: Unique ergodicity translation surfaces logarithm laws

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