Quelques remarques sur les facteurs des systèmes dynamiques gaussiens

A. Iwanik; M. Lemańczyk; T. de la Rue; J. de Sam Lazaro

Studia Mathematica (1997)

  • Volume: 125, Issue: 3, page 247-254
  • ISSN: 0039-3223

Abstract

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We study the factors of Gaussian dynamical systems which are generated by functions depending only on a finite number of coordinates. As an application, we show that for Gaussian automorphisms with simple spectrum, the partition ( X 0 ≤ 0 ) , ( X 0 > 0 ) is generating.

How to cite

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Iwanik, A., et al. "Quelques remarques sur les facteurs des systèmes dynamiques gaussiens." Studia Mathematica 125.3 (1997): 247-254. <http://eudml.org/doc/216436>.

@article{Iwanik1997,
author = {Iwanik, A., Lemańczyk, M., de la Rue, T., de Sam Lazaro, J.},
journal = {Studia Mathematica},
keywords = {Gaussian dynamical systems; ergodic Gaussian process; shift; factors; Gaussian automorphisms},
language = {fre},
number = {3},
pages = {247-254},
title = {Quelques remarques sur les facteurs des systèmes dynamiques gaussiens},
url = {http://eudml.org/doc/216436},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Iwanik, A.
AU - Lemańczyk, M.
AU - de la Rue, T.
AU - de Sam Lazaro, J.
TI - Quelques remarques sur les facteurs des systèmes dynamiques gaussiens
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 3
SP - 247
EP - 254
LA - fre
KW - Gaussian dynamical systems; ergodic Gaussian process; shift; factors; Gaussian automorphisms
UR - http://eudml.org/doc/216436
ER -

References

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  1. [1] I. P. Cornfeld, S. V. Fomin and Y. G. Sinai, Ergodic Theory, Springer, 1982. 
  2. [2] M. Lemańczyk, F. Parreau and J.-P. Thouvenot, On the disjointness problem for Gaussian automorphisms, preprint. 
  3. [3] M. Lemańczyk and F. Parreau, Gaussian automorphisms whose self-joinings are Gaussian, preprint. 
  4. [4] M. Lemańczyk and J. de Sam Lazaro, Spectral analysis of certain compact factors for Gaussian dynamical systems, Israel J. Math. (1996), à paraître. 
  5. [5] L. H. Loomis, An Introduction to Abstract Harmonic Analysis, Van Nostrand, Princeton, 1953. 
  6. [6] D. Newton, On Gaussian processes with simple spectrum, Z. Wahrsch. Verw. Gebiete 5 (1966), 207-209. 
  7. [7] D. Newton and W. Parry, On a factor automorphism of a normal dynamical system, Ann. Math. Statist. 37 (1966), 1528-1533. 
  8. [8] W. Parry, Generators in Ergodic Theory, Benjamin, New York, 1969. 
  9. [9] T. de la Rue, Entropie d’un système dynamique gaussien : cas d’une action de ℤ d , C. R. Acad. Sci. Paris Sér. I 317 (1993), 191-194. 
  10. [10] J. P. Thouvenot, Some properties and applications of joinings in ergodic theory, in: Ergodic Theory and its Connections with Harmonic Analysis, London Math. Soc. Lecture Note Ser. 205, Cambridge Univ. Press, 1995, 207-235. 
  11. [11] J. P. Thouvenot, Utilisation des processus gaussiens en théorie ergodique, preprint. 

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