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Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics

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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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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    HuaGui Duan

  2. Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Hui Liu

Authors
  1. HuaGui Duan
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  2. Hui Liu
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Correspondence to Hui Liu.

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Duan, H., Liu, H. Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics. Sci. China Math. 59, 531–538 (2016). https://doi.org/10.1007/s11425-015-5076-3

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  • DOI: https://doi.org/10.1007/s11425-015-5076-3

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