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

Tom 110 / 2008

Y. Derriennic, K. Frączek, M. Lemańczyk, F. Parreau Colloquium Mathematicum 110 (2008), 81-115 MSC: 37A05, 37A50. DOI: 10.4064/cm110-1-3

Streszczenie

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.

Autorzy

  • Y. DerriennicLaboratoire 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
    e-mail
  • K. FrączekFaculty 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
    e-mail
  • M. LemańczykFaculty 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
    e-mail
  • F. ParreauLaboratoire d'Analyse, Géométrie
    et Applications, UMR 7539
    Université Paris 13 et CNRS
    99, av. J.-B. Clément
    93430 Villetaneuse, France
    e-mail

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