Topological Mixing for Some Residual Sets of Interval Exchange Transformations

Jon Chaika; Jon Fickenscher

doi:10.1007/s00220-014-2191-x

Topological Mixing for Some Residual Sets of Interval Exchange Transformations

Jon Chaika, Jon Fickenscher

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	483-503
Number of pages	21
Journal	Communications In Mathematical Physics
Volume	333
Issue number	1
DOIs	https://doi.org/10.1007/s00220-014-2191-x
State	Published - Jan 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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title = "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.",

author = "Jon Chaika and Jon Fickenscher",

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AB - 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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Topological Mixing for Some Residual Sets of Interval Exchange Transformations

Abstract

All Science Journal Classification (ASJC) codes

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