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Sur une nil-variété, les parties minimales associées à une translation sont uniquement ergodiques

Published online by Cambridge University Press:  19 September 2008

Emmanuel Lesigne
Emmanuel Lesigne
Affiliation:
Université de Bretagne Occidental, Département de Mathématiques et Informatique, 6 Avenue he Gorgeu 29287 BREST cedex, France.
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Abstract

We call nilmanifold every compact space X on which a connected locally compact nilpotent group acts transitively. We show that, if X is a nilmanifold and f is a continuous function on X, then, for all x in X and a in N, the sequence

converges. We give a process for the computation of the limit. A similar result for the continuous means is presented.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 2 , June 1991 , pp. 379 - 391
Copyright
Copyright © Cambridge University Press 1991

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References

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