Quelques remarques sur les facteurs des systèmes dynamiques gaussiens
Iwanik, A. ; Lemańczyk, M. ; de la Rue, T. ; de Sam Lazaro, J.
Studia Mathematica, Tome 122 (1997), p. 247-254 / Harvested from The Polish Digital Mathematics Library
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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 (X0≤0),(X0>0) is generating.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216436 
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Iwanik, A.; Lemańczyk, M.; de la Rue, T.; de Sam Lazaro, J. Quelques remarques sur les facteurs des systèmes dynamiques gaussiens. Studia Mathematica, Tome 122 (1997) pp. 247-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i3p247bwm/

[00000] [1] I. P. Cornfeld, S. V. Fomin and Y. G. Sinai, Ergodic Theory, Springer, 1982.

[00001] [2] M. Lemańczyk, F. Parreau and J.-P. Thouvenot, On the disjointness problem for Gaussian automorphisms, preprint.

[00002] [3] M. Lemańczyk and F. Parreau, Gaussian automorphisms whose self-joinings are Gaussian, preprint.

[00003] [4] M. Lemańczyk and J. de Sam Lazaro, Spectral analysis of certain compact factors for Gaussian dynamical systems, Israel J. Math. (1996), à paraître.

[00004] [5] L. H. Loomis, An Introduction to Abstract Harmonic Analysis, Van Nostrand, Princeton, 1953.

[00005] [6] D. Newton, On Gaussian processes with simple spectrum, Z. Wahrsch. Verw. Gebiete 5 (1966), 207-209.

[00006] [7] D. Newton and W. Parry, On a factor automorphism of a normal dynamical system, Ann. Math. Statist. 37 (1966), 1528-1533.

[00007] [8] W. Parry, Generators in Ergodic Theory, Benjamin, New York, 1969.

[00008] [9] T. de la Rue, Entropie d’un système dynamique gaussien : cas d’une action de ℤd, C. R. Acad. Sci. Paris Sér. I 317 (1993), 191-194.

[00009] [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.

[00010] [11] J. P. Thouvenot, Utilisation des processus gaussiens en théorie ergodique, preprint.