Stability of closed geodesics on Finsler 2-spheres (Q941421)

The aim of the authors is to prove the following Theorem 2.1 On every Finsler 2-sphere with only finitely many prime geodesics, there exist always at least two irrationally elliptic prime geodesics. Their proof contains four ingredients: Morse theory, the precise index iteration formulae from [\textit{Y. Long}, Adv. Math. 154, No.~1, 76--131 (2000; Zbl 0970.37013)], existence theorems of N. Hingston and Rademacher's mean index identity. They note that the Theorem 2.1 is sharp and that one cannot hope that it holds for all Finsler 2-spheres which posses infinitely many prime closed geodesics.