# 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} }

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.

## 173 Citations

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