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arXiv · 1201.3738

Ergodic infinite group extensions of geodesic flows on translation surfaces

David Ralston·Serge Troubetzkoy
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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.

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David Ralston, Serge Troubetzkoy. 2012-01-18. Ergodic infinite group extensions of geodesic flows on translation surfaces. https://doi.org/10.3934/jmd.2012.6.477

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