The existence of two closed geodesics on every Finsler 2-sphere (Q2655160)

In this interesting and well-written paper, the authors prove that every Finsler (not necessarily reversible) metric on the unit sphere \(S^2\) admits at least two distinct prime closed geodesics, where a closed geodesic \(\gamma: S^1={\mathbb R}/{\mathbb Z}\to S^2\) is prime if it is not of the form \(\gamma(t)=\tilde\gamma(mt)\) for some integer \(m>1\) and another closed geodesic \(\tilde\gamma\). The proof depends on a careful study of the different symplectic normal forms of the linearized Poincaré map of a geodesic, and relies on previous works by \textit{N. Hingston} [Proc. Am. Math. Soc. 125, No.~10, 3099--3106 (1997; Zbl 0889.58026)] and [\textit{H.-B. Rademacher}, Morse Theorie und geschlossene Geodätische. Bonner Math. Schriften 229. Bonn: Univ. Bonn (1992; Zbl 0826.58012)].