Equidistribution of Dilations of Polynomial Curves in Nilmanifolds
نویسنده
چکیده
In this paper we study the asymptotic behaviour under dilations of probability measures supported on smooth 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 Rn-representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necessary dilation of a given smooth curve in Rn so that the canonical projection onto Tn is ε-dense.
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تاریخ انتشار 2008