A model for rank one measure preserving transformations

TL;DR

This paper introduces a new model for rank one measure preserving transformations using a Polish topology on the space of codes, showing it shares generic dynamical properties with classical systems.

Contribution

It defines a novel topological framework for symbolic rank one systems and demonstrates their dynamical equivalence to traditional measure preserving transformations.

Findings

The space of codes has the same generic properties as classical rank one transformations.

A new Polish topology on the space of codes is established.

The model captures essential dynamical features of measure preserving systems.

Abstract

We define a model for rank one measure preserving transformations in the sense of [2]. This is done by defining a new Polish topology on the space of codes, which are infinite rank one words, for symbolic rank one systems. We establish that this space of codes has the same generic dynamical properties as the space of (rank one) measure preserving transformations on the unit interval.