A symbolic representation for Anosov-Katok systems (Q2000404)

This paper is part of a series of papers leading to the following final result: if \(M\) is a torus, a disc or an annulus, then the measure-isomorphism relation among pairs of ergodic measure-preserving \(C^\infty\) diffeomorphisms of \(M\) is not a Borel set with respect to the \(C^\infty\) topology. In this paper a collection of measure-preserving transformations, called circular systems, are defined as symbolic systems constructed using a formal operation on words, the circular operator. The main result states that if \(T\) is an ergodic transformation on a standard measure space then \(T\) is isomorphic to a uniform Anosov-Katok diffeomorphism if and only if \(T\) is isomorphic to a uniform circular system.