Article Dans Une Revue Journal of modern dynamics Année : 2012

Ergodic infinite group extensions of geodesic flows on translation surfaces

Résumé

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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hal-00660902 , version 1 (18-01-2012)

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David Ralston, Serge Troubetzkoy. Ergodic infinite group extensions of geodesic flows on translation surfaces. Journal of modern dynamics, 2012, pp.477-497. ⟨10.3934/jmd.2012.6.477⟩. ⟨hal-00660902⟩
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