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Un théorème de disjonction de systèmes dynamiques et une généralisation du théorème ergodique de Wiener—Wintner

Published online by Cambridge University Press:  19 September 2008

E. Lesigne
E. Lesigne
Affiliation:
Université de Bretagne Occidentale, 6 avenue Victor Le Gorgeu, 29287- Brest Cedex, France
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Abstract

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If (Ω, μ, T) is a measure preserving system and if ƒ ∈ L1(μ) then, for almost all ω, for every real polynomial P, the sequence

To prove this result we use the concept of disjointness of dynamical systems and the fact that disjointness is preserved by isometric extensions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 3 , September 1990 , pp. 513 - 521
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[1]Bourgain, J.. Théorèmes ergodiques ponctuels pour certains ensembles arithmétiques. Note au C. R. Acad. Sci. Paris 305 (1987), 397–402.Google Scholar
[2]Furstenberg, H.. Strict ergodicity and transformations of the torus. Amer. J. Math. 83 (1961), 573–601.CrossRefGoogle Scholar
[3]Furstenberg, H.. Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation. Math. Systems Theory 1 (1967), 1–49.CrossRefGoogle Scholar
[4]Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press: 1981.CrossRefGoogle Scholar
[5]Lesigne, E.. Théorèmes ergodiques pour une translation sur une nil–variété. Ergod. Th. & Dynam. Sys. 9 (1989), 115–126.CrossRefGoogle Scholar
[6]Thouvenot, J. P.. La démonstration de Furstenberg du théorème de Szemerédi sur les progressions arithmétiques. Séminaire Bourbaki (1977/1978) no. 518.Google Scholar
[7]Wiener, N. & Wintner, A.. Harmonic analysis and ergodic theory. Amer. J. Math. 63 (1941), 415–426.CrossRefGoogle Scholar