Equidistribution of Dilations of Polynomial Curves in Nilmanifolds

Details Equidistribution of Dilations of Polynomial Curves in Nilmanifolds Equidistribution of Dilations of Polynomial Curves in Nilmanifolds

2008-09-26

arxiv.org/abs/0809.4519v4

Mathematics

Dynamical Systems

15 pages, to appear in Proceedings of AMS

Scientific paper

In this paper we study the asymptotic behaviour under dilations of probability measures supported on polynomial curves in nilmanifolds. We prove, under some mild conditions, effective equidistribution of such measures to the Haar measure. We also formulate a mean ergodic theorem for $\R^n$-representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necessary dilation of a given smooth curve in $ \R^n$ so that the canonical projection onto $ \T^n $ is $ \eps$-dense.

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