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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
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| Published: |
August 15, 2009 |
| Keywords: |
Ergodic, weak mixing, uniform rigidity |
| Subject: |
Primary 37A05; Secondary 37A15, 37B05 |
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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.
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| Acknowledgements
The authors were partially supported by NSF REU Grant DMS-0353634. The second author was also supported by NSF grant 0804357.
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| 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
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