On nonsingular Chacon transformations

Ergodic Theory: Nonsingular Transformations

Glossary 1 1. Definition of the subject and its importance 2 2. Basic Results 2 3. Panorama of Examples 8 4. Mixing notions and multiple recurrence 10 5. Topological group Aut(X,μ) 13 6. Orbit theory 15 7. Smooth nonsingular transformations 21 8. Spectral theory for nonsingular systems 22 9. Entropy and other invariants 25 10. Nonsingular Joinings and Factors 27 11. Applications. Connections wi...

Rank One Power Weakly Mixing Nonsingular Transformations

We show that Chacon's nonsingular type III transformation T , 0 < 1, is power weakly mixing, i.e., for all sequences of nonzero integers fk1; : : : ; krg, T k1 : : : T kr is ergodic. We then show that in in nite measure, this condition is not implied by in nite ergodic index (having all nite Cartesian products ergodic), and that in nite ergodic index does not imply 2-recurrence.

On nonsingular loop transformations using SUIF's dependence abstraction

Double Ergodicity of Nonsingular Transformations and In nite measure-preserving Staircase Transformations

A nonsingular transformation is said to be doubly ergodic if for all sets A and B of positive measure there exists an integer n > 0 such that (T n(A) \ A) > 0 and (T n(A) \ B) > 0. While double ergodicity is equivalent to weak mixing for nite measure-preserving transformations, we show that this is not the case for in nite measure preserving transformations. We show that all measure-preserving ...

On Factors of Nonsingular Cartesian Products

We classify all factors of the Cartesian product of any two nonsingular type III , 0 < < 1, or II1, Chacon transformations, as well as the centralizer of nite Cartesian products of such transformations. AMS 1991 subject classi cation: 28D99.