Generalized Oxtoby subshifts and hyperfiniteness

TL;DR

This paper introduces a class of symbolic subshifts capable of representing all Choquet simplices as invariant measure spaces, and demonstrates that the conjugacy relation within this class is hyperfinite, advancing understanding of dynamical systems.

Contribution

It constructs a new class of symbolic subshifts that realize all Choquet simplices and proves the conjugacy relation is hyperfinite, linking symbolic dynamics with measure-theoretic properties.

Findings

Realizes all Choquet simplices as invariant measure spaces

Shows the conjugacy relation on this class is hyperfinite

Advances the connection between symbolic dynamics and measure theory

Abstract

We show that there exists a class of symbolic subshifts which realizes all Choquet simplices as simplices of invariant measures and the conjugacy relation on that class is hyperfinite.