A brief remark on orbits of $SL(2,Z)$ in the euclidean plane

Abstract

The repartition of dense orbits of $\textrm{SL}(2,\dr Z)$ in the euclidean plane is described by Ledrappier and Nogueira. We describe here the specific patterns one can see by experimentation, linking it to diophantine approximation theory.

8 pages, 2 figures