The growth and distribution of large circles on translation surfaces

Paul Colognese, Mark Pollicott

Published 2021-07-29Version 1

We consider circles on a translation surface $X$, consisting of points joined to a common center point by a geodesic of length $R$. We show that as $R \to \infty$ these circles distribute to a measure on $X$ which is equivalent to the area. In the last section we consider analogous results for closed geodesics.