English

On ergodic transformations that are both weakly mixing and uniformly rigid

Dynamical Systems 2009-03-14 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0809.4406,
  title  = {On ergodic transformations that are both weakly mixing and uniformly rigid},
  author = {Jennifer James and Thomas Koberda and Kathryn Lindsey and Cesar E. Silva and Peter Speh},
  journal= {arXiv preprint arXiv:0809.4406},
  year   = {2009}
}

Comments

Revised version after referee's report

R2 v1 2026-06-21T11:24:09.682Z