Mild mixing of certain interval exchange transformations

TL;DR

This paper proves that certain interval exchange transformations with specific recurrence properties are always mildly mixing, and shows that the set of such transformations is large in a fractal dimension sense.

Contribution

It establishes that irreducible, linearly recurrent, type W interval exchange transformations are always mildly mixing, expanding understanding of their dynamical behavior.

Findings

All irreducible, linearly recurrent, type W interval exchange transformations are mildly mixing.

The set of such transformations has full Hausdorff dimension for every irreducible permutation.

The results connect recurrence properties with mixing behavior in interval exchange transformations.

Abstract

We prove that irreducible, linearly recurrent, type W interval exchange transformations are always mild mixing. For every irreducible permutation the set of linearly recurrent interval exchange transformations has full Hausdorff dimension.