On Mixing Rank One Infinite Transformations

Abstract

J.-P. Thouvenot and the author showed via different approaches that the centralizer of a mixing rank-one infinite measure preserving transformation was trivial. In this note the author presents his joining proof. We also consider constructions with algebraic spacers as well as a class of Sidon constructions to produce new examples of mixing rank one transformations. In connection with Gordin's question on the existence of homoclinic ergodic actions for a zero entropy system we also discuss Poisson suspensions of some modifications of Sidon rank one constructions.

References in corpus (1)

• On ergodic properties of iceberg transformations. I: Approximation and spectral multiplicity

Cited by in corpus (5)

• Prime Poisson suspensions
• On Mixing Constructions with Algebraic Spacers
• Simple Spectrum for Tensor Products of Mixing Map Powers
• Singular Schaeffer-Salem measures of dynamical system origin
• Subsequence Rational Ergodicity of Rank-One Transformations