On ergodic transformations that are both weakly mixing and uniformly rigid

Details On ergodic transformations that are both weakly mixing and uniformly rigid On ergodic transformations that are both weakly mixing and uniformly rigid

2008-09-25

arxiv.org/abs/0809.4406v2

Mathematics

Dynamical Systems

Revised version after referee's report

Scientific paper

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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