Equidistribution of dilations of polynomial curves in nilmanifolds

Authors:
Michael Björklund and Alexander Fish

Journal:
Proc. Amer. Math. Soc. **137** (2009), 2111-2123

MSC (2000):
Primary 60B15

DOI:
https://doi.org/10.1090/S0002-9939-09-09836-0

Published electronically:
January 27, 2009

MathSciNet review:
2480293

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Abstract: 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, the effective equidistribution of such measures to the Haar measure. We also formulate a mean ergodic theorem for -representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necessary dilation of a given smooth curve in so that the canonical projection onto is -dense.

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Additional Information

**Michael Björklund**

Affiliation:
Department of Mathematics, KTH - Royal Institute of Technology, SE-100 44 Stockholm, Sweden

Email:
mickebj@math.kth.se

**Alexander Fish**

Affiliation:
Department of Mathematics, Ohio State University, Columbus, Ohio 43210

Email:
afish@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9939-09-09836-0

Received by editor(s):
September 5, 2008

Published electronically:
January 27, 2009

Additional Notes:
The research of the second author was partly done during his visit to MSRI, Berkeley

Communicated by:
Bryna Kra

Article copyright:
© Copyright 2009
American Mathematical Society