On ergodic transformations that are both weakly mixing and uniformly rigid

Jennifer James, Thomas Koberda, Kathryn Lindsey, Cesar E. Silva, Peter Speh

Published 2008-09-25, updated 2009-03-14Version 2

We examine some of the properties of uniformly rigid transformations, and analyze the compatibility of uniform rigidity and (measurable) weak mixing along with some of their asymptotic convergence properties. We show that on Cantor space, there does not exist a finite measure-preserving, totally ergodic, uniformly rigid transformation. We briefly discuss general group actions and show that (measurable) weak mixing and uniform rigidity can coexist in a more general setting.