A Transversal for horocycle flow on H(2)
Abstract
Using zippered rectangle coordinates we parametrize a Poincar\'e section for horocycle flow on the space of genus 2 translation surfaces with one singular cone point of angle 6π. In addition, we bound the return time under horocycle flow to this Poincar\'e section by examining a subset of surfaces where a certain sum of parameters is large.
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