Abstract: | If all prime closed geodesics on (Sn, F) with an irreversible Finsler metric F are irrationally elliptic, there exist either exactly 2 \(\left {\frac{{n + 1}}{2}} \right]\) or infinitely many distinct closed geodesics. As an application, we show the existence of three distinct closed geodesics on bumpy Finsler (S3, F) if any prime closed geodesic has non-zero Morse index. |