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Topological Mixing for Some Residual Sets of Interval Exchange Transformations

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Abstract

We show that a residual set of non-degenerate IETs on more than 3 letters is topologically mixing. This shows that there exists a uniquely ergodic topologically mixing IET. This is then applied to show that some billiard flows in a fixed direction in an L-shaped polygon are topologically mixing.

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Authors and Affiliations

  1. University of Utah, Salt Lake City, USA

    Jon Chaika

  2. Princeton University, Princeton, USA

    Jon Fickenscher

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  1. Jon Chaika
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  2. Jon Fickenscher
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Correspondence to Jon Fickenscher.

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Communicated by M. Lyubich

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Chaika, J., Fickenscher, J. Topological Mixing for Some Residual Sets of Interval Exchange Transformations. Commun. Math. Phys. 333, 483–503 (2015). https://doi.org/10.1007/s00220-014-2191-x

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  • DOI: https://doi.org/10.1007/s00220-014-2191-x

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