Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics (Q295098)

The authors study the multiplicity problem on the Finsler sphere \((S^n, F)\) with irrationally elliptic closed geodesics. The main result of the paper is: ``If all prime closed geodesics on \((S^n, F)\) with an irreversible Finsler metric \(F\) are irrationally elliptic, there exist either exactly \(2[\frac{n+1}{2}]\) or infinitely many distinct closed geodesics.'' As an application of this result, the authors show that ``there exist at least three distinct closed geodesics on a bumpy Finsler \((S^3, F)\) if any prime closed geodesic on it has a non-zero Morse index.''