A symbolic representation of Anosov-Katok systems

TL;DR

This paper introduces new symbolic representations for Anosov-Katok diffeomorphisms, advancing understanding of measure-preserving systems and their realizability as smooth diffeomorphisms on compact manifolds.

Contribution

It provides novel symbolic models for Anosov-Katok systems, contributing to the classification and realization problems in smooth dynamical systems.

Findings

New symbolic representations of Anosov-Katok diffeomorphisms

Progress towards classifying measure-preserving diffeomorphisms

Insights into realizability of systems as smooth diffeomorphisms

Abstract

This paper is part 1 of a series of papers culminating in the result that measure preserving diffeomorphisms of the disc or 2-torus are unclassifiable. It also addresses another classical problem: which abstract measure preserving systems are realizable as smooth diffeomorphisms of a compact manifold? The main result of this paper gives new symbolic representations of the Anosov-Katok diffeomorphisms.