Ergodic infinite group extensions of geodesic flows on translation surfaces
Dynamical Systems
2013-01-09 v1
Abstract
We show that generic infinite group extensions of geodesic flows on square tiled translation surfaces are ergodic in almost every direction, subject to certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown that certain concrete staircases, covers of square-tiled surfaces, are not ergodic in almost every direction. In contrast we show the almost sure ergodicity of other concrete staircases. An appendix provides a combinatorial approach for the study of square-tiled surfaces.
Cite
@article{arxiv.1201.3738,
title = {Ergodic infinite group extensions of geodesic flows on translation surfaces},
author = {David Ralston and Serge Troubetzkoy},
journal= {arXiv preprint arXiv:1201.3738},
year = {2013}
}