Equidistribution of dilations of polynomial curves in nilmanifolds
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- by Michael Björklund and Alexander Fish PDF
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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 $\mathbb {R}^n$-representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necessary dilation of a given smooth curve in $\mathbb {R}^n$ so that the canonical projection onto $\mathbb {T}^n$ is $\varepsilon$-dense.References
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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
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2111-2123
- MSC (2000): Primary 60B15
- DOI: https://doi.org/10.1090/S0002-9939-09-09836-0
- MathSciNet review: 2480293