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- W2890419900 abstract "We study the general problem of equidistribution of expanding translates of an analytic curve by an algebraic diagonal flow on the homogeneous space $G/Gamma$ of a semisimple algebraic group $G$. We define two families of algebraic subvarieties of the associated partial flag variety $G/P$, which give the obstructions to non-divergence and equidistribution. We apply this to prove that for Lebesgue almost every point on an analytic curve in the space of $mtimes n$ real matrices whose image is not contained in any subvariety coming from these two families, the Dirichlet's theorem on simultaneous Diophantine approximation cannot be improved. The proof combines geometric invariant theory, Ratner's theorem on measure rigidity for unipotent flows, and linearization technique." @default.
- W2890419900 created "2018-09-27" @default.
- W2890419900 creator A5011333604 @default.
- W2890419900 date "2018-09-22" @default.
- W2890419900 modified "2023-10-14" @default.
- W2890419900 title "Equidistribution of expanding translates of curves and Diophantine approximation on matrices" @default.
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- W2890419900 doi "https://doi.org/10.48550/arxiv.1809.08515" @default.
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