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

Volume 15

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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
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.
Acknowledgements

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
jjames@brandeis.edu

Thomas Koberda:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
koberda@math.harvard.edu

Kathryn Lindsey:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
klindsey@math.cornell.edu

Cesar E. Silva:
Department of Mathematics, Williams College, Williamstown, MA 01267, USA
csilva@williams.edu

Peter Speh:
Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139, USA
pspeh@math.mit.edu