Slope Gap Distribution of Saddle Connections on the 2n-gon
Geometric Topology
2024-06-14 v2 Dynamical Systems
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.
Cite
@article{arxiv.2109.04495,
title = {Slope Gap Distribution of Saddle Connections on the 2n-gon},
author = {Jonah Berman and Taylor McAdam and Ananth Miller-Murthy and Caglar Uyanik and Hamilton Wan},
journal= {arXiv preprint arXiv:2109.04495},
year = {2024}
}
Comments
51 pages, 34 figures. v2: Incorporates referee comments, improves upper bound and provides high level summaries at various points