No. 2025.09
Quadratic growth of geodesics on the two-sphere
B. Albach
Subject: Symplectic geometry
Abstract
We prove that for any reversible Finsler metric on $S^2$, 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.