Gaussian automorphisms whose ergodic self-joinings are Gaussian

Mariusz Lemańczyk; F. Parreau; J. Thouvenot

Fundamenta Mathematicae (2000)

  • Volume: 164, Issue: 3, page 253-293
  • ISSN: 0016-2736

Abstract

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 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.

How to cite

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Lemańczyk, Mariusz, Parreau, F., and Thouvenot, J.. "Gaussian automorphisms whose ergodic self-joinings are Gaussian." Fundamenta Mathematicae 164.3 (2000): 253-293. <http://eudml.org/doc/212456>.

@article{Lemańczyk2000,
abstract = {  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. },
author = {Lemańczyk, Mariusz, Parreau, F., Thouvenot, J.},
journal = {Fundamenta Mathematicae},
keywords = {Gaussian space; Gaussian automorphism; Gaussian joining; ergodic self-joinings},
language = {eng},
number = {3},
pages = {253-293},
title = {Gaussian automorphisms whose ergodic self-joinings are Gaussian},
url = {http://eudml.org/doc/212456},
volume = {164},
year = {2000},
}

TY - JOUR
AU - Lemańczyk, Mariusz
AU - Parreau, F.
AU - Thouvenot, J.
TI - Gaussian automorphisms whose ergodic self-joinings are Gaussian
JO - Fundamenta Mathematicae
PY - 2000
VL - 164
IS - 3
SP - 253
EP - 293
AB -  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.
LA - eng
KW - Gaussian space; Gaussian automorphism; Gaussian joining; ergodic self-joinings
UR - http://eudml.org/doc/212456
ER -

References

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