Ergodic infinite group extensions of geodesic flows on translation surfaces

David Ralston; Serge Troubetzkoy

doi:10.3934/jmd.2012.6.477

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2012, Volume 6, Issue 4: 477-497. Doi: 10.3934/jmd.2012.6.477

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Ergodic infinite group extensions of geodesic flows on translation surfaces

David Ralston^1, and
Serge Troubetzkoy^2,

1.
SUNY College at Old Westbury, Mathematics/CIS Department, P.O. Box 210, Old Westbury, NY 11568
2.
Aix-Marseille University, CNRS, CPT, IML, Frumam, 13288 Marseille Cedex 09

Received: April 30, 2012

Published: December 2012

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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. 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.

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

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