Two closed geodesics on compact bumpy Finsler manifolds
In this paper, we prove there are at least two closed geodesics on any compact bumpy Finsler $n$ manifold with $n\ge 2$ Thus generically there are at least two closed geodesics on compact Finsler manifolds. Furthermore, there are at least two closed geodesics on any compact Finsler $2$ manifold, and this lower bound is achieved by the Katok 2 sphere, cf. \cite{Kat}