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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