Approximation of points in the plane by generic lattice orbits
  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 $\Gamma<\mathrm{SL}_2(\mathbb{R})$ acting linearly on $\mathbb{R}^2$. Our method gives bounds that are uniform for almost all orbits. 
Dubi Kelmer
math.NT