EVENT DETAILS AND ABSTRACT

Title: Embedding into toral automorphisms
Speaker: Anthony Quas
Speaker Info: University of Victoria
Brief Description:
Special Note:
Abstract:

The Krieger Generator Theorem may be thought of as saying that given a full shift with topological entropy H, then for any (aperiodic ergodic) measure-preserving transformation with measure-theoretic entropy h less than H, there exists an embedding (a dynamics-preserving injection) from the measure-preserving system to the full shift. This property is known as universality. Krieger also proved that irreducible shifts of finite are universal. In this talk, I will discuss universality of toral automorphisms. In particular, the case where the automorphism has an eigenvalue on the unit circle is of interest, and relates to work of Lindenstrauss and Schmidt. The central technique is a formulation of Ornstein theory due to Burton and Rothstein. This is joint work with Terry Soo.