American Institute of Mathematical Sciences

2017, 11: 143-153. doi: 10.3934/jmd.2017007

Approximation of points in the plane by generic lattice orbits

 Department of Mathematics, Maloney Hall, Boston College, Chestnut Hill, MA 02467-3806, USA

Received  June 29, 2016 Revised  December 04, 2016 Published  February 2017

Fund Project: Partially supported by NSF grant DMS-1401747.

We give upper and lower bounds for Diophantine exponents measuring how well a point in the plane can be approximated by points in the orbit of a lattice $\Gamma < {\rm{S}}{{\rm{L}}_2}\left( {\mathbb{R}} \right)$ acting linearly on ${\mathbb{R}^2}$. Our method gives bounds that are uniform for almost all orbits.

Citation: Dubi Kelmer. Approximation of points in the plane by generic lattice orbits. Journal of Modern Dynamics, 2017, 11: 143-153. doi: 10.3934/jmd.2017007
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References:
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