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Systèmes dynamiques gaussiens d'entropie nulle, lâchement et non lâchement Bernoulli

Published online by Cambridge University Press:  19 September 2008

Thierry De La Rue
Thierry De La Rue
Affiliation:
Analyse et Modèles Stochastiques, URA-CNRS 1378, Université de Rouen 76130 Mont-Saint-Aignan, France
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Abstract

We construct two real Gaussian dynamical systems of zero entropy; the first one is not loosely Bernoulli, and the second is a loosely Bernoulli Gaussian-Kronecker system. To get loose-Bernoullicity for the second system, we prove and use a property of planar Brownian motion on [0, 1]: we can recover the whole trajectory knowing only some angles formed by the motion.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 2 , April 1996 , pp. 379 - 404
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

[1]Cornfeld, I. P., Fomin, S. V. et Sinai, Ya. G.. Ergodic Theory. Springer, Berlin, 1982.CrossRefGoogle Scholar
[2]Junco, A. Del. Transformations with discrete spectrum are stacking transformations. Canad. J. Math. 28 (1976), 836–839.CrossRefGoogle Scholar
[3]Feldman, J.. New K-automorphisms and a problem of Kakutani. Isr. J. Math. 24 (1976), 16–38.CrossRefGoogle Scholar
[4]Ferenczi, S.. Systèmes de rang fini. Thèse de doctorat d'État, Université d'Aix-Marseille 2, 1990.Google Scholar
[5]Iwanik, A. et De Sam Lazaro, J.. Sur la multiplicité Lp d'un automorphisme gaussien. C. R. Acad. Sci. Paris, Série I 312 (1991), 875–876.Google Scholar
[6]King, J.. The commutant is the weak closure of the powers, for rank-1 transformations. Ergod. Th. & Dynam. Sys. 6 (1986), 363–384.CrossRefGoogle Scholar
[7]Ornstein, D. S., Rudolph, D. J. et Weiss, B.. Equivalence of Measure Preserving Transformations. Memoirs of the American Mathematical Society 262. Amer. Math. Soc., 1982.Google Scholar
[8]Rothstein, A.. Vershik processes: First steps. Isr. J. Math. 36 (1980), 205–224.Google Scholar
[9]de la Rue, T.. Entropie d'un système dynamique gaussien: Cas d'une action de . C. R. Acad. Sci. Paris, Série I 317 (1993), 191–194.Google Scholar
[10]de la Rue, T.. Mouvement moyen et système dynamique gaussien. Probab. Theory Relat. Fields 102 (1995), 45–56.CrossRefGoogle Scholar
[11]Thouvenot, J. P.. The metrical structure of some Gaussian processes. In Ergodic Theory and Related Topics II, pp 195–198, Georgenthal, 1986. Teubner Texte zur Mathematik.Google Scholar