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arXiv · 1004.1326

Approximation to points in the plane by SL(2,Z)-orbits

Michel Laurent·Arnaldo Nogueira
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Abstract

Let x be a point in R^2 with irrational slope and let Γdenote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit Γx is dense in R^2. We give efective results on the approximation of a point y in R^2 by points of the form γx, where γbelongs to Γ, in terms of the size of γ.

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Michel Laurent, Arnaldo Nogueira. 2010-04-08. Approximation to points in the plane by SL(2,Z)-orbits. https://doi.org/10.1112/jlms%2Fjdr061

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