Quadratic growth of geodesics on the two-sphere
Symplectic Geometry
2026-03-09 v3
Abstract
We prove that for any reversible Finsler metric on S2, the number of prime closed geodesics grows quadratically with respect to length. The main tools are an improvement on Franks' theorem about the number of periodic points of area-preserving annulus maps, and the theory of cylindrical contact homology in the complement of a link.
Cite
@article{arxiv.2508.00147,
title = {Quadratic growth of geodesics on the two-sphere},
author = {Bernhard Albach},
journal= {arXiv preprint arXiv:2508.00147},
year = {2026}
}
Comments
39 pages. V3 minor rewrites, results unchanged