Counting Closed Geodesics in Rank 1 $\mathrm{SL}\left(2,\mathbb{R}\right)$-orbit Closures
Geometric Topology
2022-07-04 v1 Dynamical Systems
Abstract
We obtain bounds on the numbers of intersections between triangulations as the conformal structure of a surface varies along a Teichm{\"u}ller geodesic contained in an -orbit closure of rank 1 in the moduli space of Abelian differentials. For , we obtain an exponential bound on the number of closed geodesics in the orbit closure, of length at most , that spend at least -fraction of their length in a region with short saddle connections.
Keywords
Cite
@article{arxiv.2207.00073,
title = {Counting Closed Geodesics in Rank 1 $\mathrm{SL}\left(2,\mathbb{R}\right)$-orbit Closures},
author = {John Rached},
journal= {arXiv preprint arXiv:2207.00073},
year = {2022}
}