Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold

@article{Leibman2004PointwiseCO,
title={Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold},
author={Alexander Leibman},
journal={Ergodic Theory and Dynamical Systems},
year={2004},
volume={25},
pages={201 - 213}
}
• A. Leibman
• Published 22 December 2004
• Mathematics
• Ergodic Theory and Dynamical Systems
We show that the orbit of a point on a compact nilmanifold X under the action of a polynomial sequence of translations on X is well distributed on the union of several sub-nilmanifolds of X. This implies that the ergodic averages of a continuous function on X along a polynomial sequence of translations on X converge pointwise.
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