Ergodic Theory and Dynamical Systems

Research Article

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

Emmanuel Lesignea1

a1 Université de Bretagne Occidental, Département de Mathématiques et Informatique, 6 Avenue he Gorgeu 29287 BREST cedex, France.


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.

(Received May 08 1989)

(Revised July 20 1990)