Strict Doubly Ergodic Infinite Transformations

2015/12/31 by Loh, Isaac, Silva, Cesar E.
#37A25 (Secondary) #37A40 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.09340

Abstract

We give examples of rank-one transformations that are (weak) doubly ergodic and rigid (so all their cartesian products are conservative), but with non-ergodic 2-fold cartesian product. We give conditions for rank-one infinite measure-preserving transformations to be (weak) doubly ergodic and for their k-fold cartesian product to be conservative. We also show that a (weak) doubly ergodic nonsingular group action is ergodic with isometric coefficients, and that the latter strictly implies W measurable sensitivity.

Related

• Ergodicity and Conservativity of products of infinite transformations\n and their inverses
• On Infinite Transformations with Maximal Control of Ergodic Two-fold\n Product Powers
• Infinite symmetric ergodic index and related examples in infinite measure
• On ergodic transformations that are both weakly mixing and uniformly rigid
• On measure-preserving rank one transformations