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arXiv · 2309.00211

Multiple closed geodesics on Finsler $3$-dimensional sphere

Huagui Duan·Zihao Qi
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Abstract

In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on $S^3$ with exactly four prime closed geodesics. And then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler $S^3$. In this paper, we proved this conjecture for bumpy Finsler $S^{3}$ if the Morse index of any prime closed geodesic is nonzero.

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Huagui Duan, Zihao Qi. 2023-09-01. Multiple closed geodesics on Finsler $3$-dimensional sphere. https://arxiv.org/abs/2309.00211

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