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Residual generic ergodicity of periodic group extensions over translation surfaces

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An Erratum to this article was published on 03 December 2016

Abstract

Continuing the work in Ralston and Troubetzkoy (J Mod Dyn 6:477–497, 2012), we show that within each stratum of translation surfaces, there is a residual set of surfaces for which the geodesic flow in almost every direction is ergodic for almost-every periodic group extension produced using a technique referred to as cuts.

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Acknowledgements

We thank the anonymous referee for detailed comments which greatly improved the presentation of this article.

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Authors and Affiliations

  1. Mathematics/CIS Department, SUNY College at Old Westbury, P.O. Box 210, Old Westbury, NY, 11568, USA

    David Ralston

  2. Aix Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France

    Serge Troubetzkoy

  3. I2M, Luminy, Case 907, 13288, Marseille CEDEX 9, France

    Serge Troubetzkoy

Authors
  1. David Ralston
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  2. Serge Troubetzkoy
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Corresponding author

Correspondence to Serge Troubetzkoy.

Additional information

The original version of the article was revised: figure 3 has been corrected.

This work was partially supported by ANR Perturbations.

An erratum to this article is available at http://dx.doi.org/10.1007/s10711-016-0211-z.

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Ralston, D., Troubetzkoy, S. Residual generic ergodicity of periodic group extensions over translation surfaces. Geom Dedicata 187, 219–239 (2017). https://doi.org/10.1007/s10711-016-0198-5

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