Topological mixing for some residual sets of interval exchange transformations

TL;DR

This paper demonstrates that a residual set of non-degenerate interval exchange transformations (IETs) with more than three letters are topologically mixing, and applies this to certain billiard flows in L-shaped polygons.

Contribution

It proves the existence of a residual set of topologically mixing, uniquely ergodic IETs with more than three letters, and applies this to billiard flow dynamics.

Findings

Residual set of non-degenerate IETs are topologically mixing

Existence of uniquely ergodic, topologically mixing IETs

Certain billiard flows in L-shaped polygons are topologically mixing

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.