Weak mixing for compact Lie extensions of interval exchange transformations

TL;DR

This paper proves that for a typical interval exchange transformation and a compact Lie group, the associated skew product is weakly mixing, extending understanding of dynamical properties in these systems.

Contribution

It establishes weak mixing for skew products of typical interval exchange transformations with compact Lie groups, a novel result in dynamical systems theory.

Findings

Weak mixing holds for typical IETs with compact Lie group extensions.

The result applies to non-rotation IETs with constant group-valued functions.

Provides new insights into the ergodic properties of IET extensions.

Abstract

We prove that for any compact connected Lie group G and a typical interval exchange transformation T, not isomorphic to a rotation, the skew product of T with a typical G-valued function, constant on the intervals, is weakly mixing.