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Ergodic infinite group extensions of geodesic flows on translation surfaces

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  • 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. K. Frączek 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.
    Mathematics Subject Classification: Primary: 37A25, 37A40; Secondary: 37A20, 37C40.


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