Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres

Abstract

We prove that for every $\Q$-homological Finsler 3-sphere $(M,F)$ with a bumpy and irreversible metric $F$, either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.

17 pages. Some modifications have been made. accepted by Calc. Var. & PDEs