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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