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

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

doi:10.4064/cm110-1-3

Geodesic

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

Y. Derriennic ¹ ; K. Frączek ² ; M. Lemańczyk ³ ; F. Parreau ⁴

¹ Laboratoire de Mathématiques de Brest associé au CNRS (Unite Mixte de Recherche no. 6205) Université de Bretagne Occidentale 6, av. Victor Le Gorgeu, CS 93837 F-29238 Brest Cedex 3, France
² Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland and Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
³ Faculty of Mathematics and Computer Science Nicolaus Copernicus University ul. Chopina 12/18 87-100 Toruń, Poland and Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
⁴ Laboratoire d'Analyse, Géométrie et Applications, UMR 7539 Université Paris 13 et CNRS 99, av. J.-B. Clément 93430 Villetaneuse, France

Colloquium Mathematicum, Tome 110 (2008) no. 1, pp. 81-115.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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 $\alpha $-stable processes are shown to belong to the ELF class.

DOI : 10.4064/cm110-1-3

Keywords: basic ergodic properties elf class automorphisms class ergodic automorphisms whose weak closure measures supported graphs iterates consists ergodic self joinings investigated disjointness elf class fold simple automorphisms interval exchange transformations given special type permutations time one maps measurable flows discussed ergodic poisson suspension automorphisms dynamical systems determined stationary ergodic symmetric alpha stable processes shown belong elf class

Affiliations des auteurs :

Y. Derriennic ¹ ; K. Frączek ² ; M. Lemańczyk ³ ; F. Parreau ⁴

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Y. Derriennic; K. Frączek; M. Lemańczyk; F. Parreau. Ergodic automorphisms whose weak closure
 of off-diagonal measures consists of ergodic
 self-joinings. Colloquium Mathematicum, Tome 110 (2008) no. 1, pp. 81-115. doi : 10.4064/cm110-1-3. http://geodesic.mathdoc.fr/articles/10.4064/cm110-1-3/

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