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Pointwise convergence of ergodic averages for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold

Published online by Cambridge University Press:  22 December 2004

A. LEIBMAN
A. LEIBMAN
Affiliation:
Department of Mathematics, The Ohio State University, OH 43221, USA (e-mail: leibman@math.ohio-state.edu)
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Abstract

Generalizing the one-parameter case, we prove that the orbit of a point on a compact nilmanifold X under a polynomial action of $\mathbb{Z}^{d}$ by translations on X is uniformly distributed on the union of several sub-nilmanifolds of X. As a corollary we obtain the pointwise ergodic theorem for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 1 , February 2005 , pp. 215 - 225
Copyright
2004 Cambridge University Press

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