A Transversal for horocycle flow on H(2)

Abstract

Using zippered rectangle coordinates we parametrize a Poincaré section for horocycle flow on the space of genus 2 translation surfaces with one singular cone point of angle $6\pi$. In addition, we bound the return time under horocycle flow to this Poincaré section by examining a subset of surfaces where a certain sum of parameters is large.

28 pages, 4 figures