Odometer Based Systems

TL;DR

This paper introduces odometer based construction sequences as a method to represent finite entropy systems with odometer factors, extending symbolic dynamics and cut-and-stack constructions without spacers.

Contribution

It demonstrates that systems with odometer factors can be represented by odometer based construction sequences, satisfying the small word condition uniformly.

Findings

Representation of finite entropy systems with odometer factors

Extension of symbolic representations of cut-and-stack constructions

Uniform satisfaction of the small word condition

Abstract

Construction sequences are a general method of building symbolic shifts that capture cut-and-stack constructions and are general enough to give symbolic representations of Anosov-Katok diffeomorphisms. We show here that any finite entropy system that has an odometer factor can be represented as a special class of construction sequences, the odometer based construction sequences which correspond to those cut-and-stack constructions that do not use spacers. We also show that any additional property called the "small word condition" can also be satisfied in a uniform way.