Asymptotic Pairs for Interval Exchange Transformations

TL;DR

This paper characterizes asymptotic pairs in the subshift of interval exchange transformations and proves that doubly asymptotic pairs are generally absent, enhancing understanding of their long-term dynamical behavior.

Contribution

It offers a new simple description of asymptotic pairs and establishes the non-existence of doubly asymptotic pairs under broad conditions.

Findings

Asymptotic pairs are characterized in the subshift of interval exchange transformations.

Doubly asymptotic pairs do not occur under general conditions.

Provides insights into the long-term dynamics of interval exchange transformations.

Abstract

We provide a simple description of asymptotic pairs in the subshift associated with an interval exchange transformation and show that, under reasonably general conditions, doubly asymptotic pairs do not occur.