Slope Gap Distribution of Saddle Connections on the 2n-gon
arXiv:2109.04495 · doi:10.3934/dcds.2022141
Abstract
We explicitly compute the limiting slope gap distribution for saddle connections on any 2n-gon. Our calculations show that the slope gap distribution for a translation surface is not always unimodal, answering a question of Athreya. We also give linear lower and upper bounds for number of non-differentiability points as n grows. The latter result exhibits the first example of a non-trivial bound on an infinite family of translation surfaces and answers a question by Kumanduri-Sanchez-Wang.
51 pages, 34 figures. v2: Incorporates referee comments, improves upper bound and provides high level summaries at various points