An algorithm to identify automorphisms which arise from self-induced interval exchange transformations

TL;DR

This paper presents an algorithm to identify when a positive automorphism of a free group corresponds to a self-induced interval exchange transformation, providing a practical method to find the associated transformation if it exists.

Contribution

The authors develop the first effective algorithm to detect and construct self-induced interval exchange transformations from positive automorphisms of free groups.

Findings

Algorithm successfully identifies when automorphisms correspond to interval exchange transformations.

Effective construction of the interval exchange transformation when the automorphism arises from it.

Provides a computational tool for studying dynamical systems related to free group automorphisms.

Abstract

We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval exchange transformation in case of success.