Affine mappings of translation surfaces: shrinking targets and Diophantine properties

Chris Judge, Josh Southerland

Let $(X,\ddot{I}‰)$ be a translation surface whose Veech group $\hat{I}“$ is a lattice. We prove that the generic orbit of the group of affine homeomorphisms of $(X,\ddot{I}‰)$ can be used to approxim…