Logarithmic laws and unique ergodicity
Dynamical Systems
2023-05-26 v2 Geometric Topology
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 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.
Cite
@article{arxiv.1603.00076,
title = {Logarithmic laws and unique ergodicity},
author = {Jon Chaika and Rodrigo Treviño},
journal= {arXiv preprint arXiv:1603.00076},
year = {2023}
}
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24 pages