Infinite Interval Exchange Transformations from Shifts

TL;DR

This paper demonstrates that minimal shifts with zero topological entropy are topologically conjugate to generally infinite interval exchange transformations, with special properties when the shifts have linear factor complexity.

Contribution

It establishes a topological conjugacy between minimal zero-entropy shifts and infinite interval exchange transformations, highlighting properties linked to linear factor complexity.

Findings

Minimal shifts with zero entropy are conjugate to infinite interval exchanges.

Linear factor complexity implies strong finiteness properties of the conjugate exchanges.

The work bridges symbolic dynamics and interval exchange transformations.

Abstract

We show that minimal shifts with zero topological entropy are topologically conjugate to interval exchange transformations, generally infinite. When these shifts have linear factor complexity (linear block growth), the conjugate interval exchanges are proved to satisfy strong finiteness properties.