On Mixing Rank One Infinite Transformations

2011/06/23 by Ryzhikov, V. V.
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1106.4655

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.

Related

• Ergodic Homoclinic Groups, Infinite Sidon Constructions and Poisson\n Suspensions
• Mixing sets for rigid transformations
• Typical infinite mixing automorphisms are rank-one
• Chacon's Type Ergodic Transformations with Unbounded Arithmetic Spacers
• Mixing on a class of rank one transformations