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arXiv · 1504.07007

On the multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics

Huagui Duan·Hui Liu
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Abstract

If all prime closed geodesics on $(S^n,F)$ 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 $(S^3,F)$ if any prime closed geodesic has non-zero Morse index.

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Huagui Duan, Hui Liu. 2015-04-27. On the multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics. https://doi.org/10.1007/s11425-015-5076-3

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