Topological mixing for some residual sets of interval exchange transformations

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.

Update to include revisions based on referee's comments. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-014-2191-x

References in corpus (3)

• Diophantine properties of IETs and general systems: Quantitative proximality and connectivity
• Self-Inverses, Lagrangian Permutations and Minimal Interval Exchange Transformations with Many Ergodic Measures
• Schrödinger Operators Defined by Interval Exchange Transformations

Cited by in corpus (1)

• Whirly 3-Interval Exchange Transformations