New York Journal of Mathematics
Volume 15 (2009) 393-403


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

On ergodic transformations that are both weakly mixing and uniformly rigid

Published: August 15, 2009
Keywords: Ergodic, weak mixing, uniform rigidity
Subject: Primary 37A05; Secondary 37A15, 37B05

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.


The authors were partially supported by NSF REU Grant DMS-0353634. The second author was also supported by NSF grant 0804357.

Author information

Jennifer James:
Department of Mathematics, Brandeis University, Waltham, MA 02454, USA

Thomas Koberda:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

Kathryn Lindsey:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA

Cesar E. Silva:
Department of Mathematics, Williams College, Williamstown, MA 01267, USA

Peter Speh:
Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139, USA