Shrinking targets for affine self-diffeomorphisms of translation surfaces
Vortrag von Prof. Dr. Chris Judge
Datum: 26.02.25 Zeit: 13.30 - 14.30 Raum: ETH HG E 33.1
The affine self-diffeomorphism group of a translation surface can be rather large. For example, the affine diffeos of a 2-torus contain a lattice. In the case of a torus $T$, Ghosh, Gorodnik, and Nevo proved that for any $\eta > 0$, for almost every $y \in T$ and for every $x \in T$, there exist infinitely many $\gamma \in SL_2(Z)$ so that $\| \gamma x- y \|\leq \|\gamma\|^{-1-\eta}$. We show that a similar result holds for translation surfaces with the lattice property. This is joint work with Josh Southerland.