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Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings

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Derriennic Y., Frączek K., Lemańczyk M., Parreau F.

Colloquium Mathematicum

2008

tom 110

nr 1

81-115

Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems determined by stationary ergodic symmetric α-stable processes are shown to belong to the ELF class.

Gaussian automorphisms whose ergodic self-joinings are Gaussian

100%

Lemańczyk M., Parreau F., Thouvenot J. P.

Fundamenta Mathematicae

2000

tom 164

nr 3

253-293

We study ergodic properties of the class of Gaussian automorphisms whose ergodic self-joinings remain Gaussian. For such automorphisms we describe the structure of their factors and of their centralizer. We show that Gaussian automorphisms with simple spectrum belong to this class. We prove a new sufficient condition for non-disjointness of automorphisms giving rise to a better understanding of Furstenberg's problem relating disjointness to the lack of common factors. This and an elaborate study of isomorphisms between classical factors of Gaussian automorphisms allow us to give a complete solution of the disjointness problem between a Gaussian automorphism whose ergodic self-joinings remain Gaussian and an arbitrary Gaussian automorphism.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Lemańczyk M.

2 Parreau F.

1 Derriennic Y.

1 Frączek K.

1 Thouvenot J. P.

1 2008

1 2000

Wyniki wyszukiwania

Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings

Gaussian automorphisms whose ergodic self-joinings are Gaussian