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arXiv · 2201.10975

Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics

Huagui Duan·Dong Xie
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Abstract

Let $M$ be a compact simply connected manifold satisfying $H^*(M;\mathbf{Q})\cong T_{d,n+1}(x)$ for integers $d\ge 2$ and $n\ge 1$. If all prime closed geodesics on $(M,F)$ with an irreversible bumpy Finsler metric $F$ are elliptic, either there exist exactly $\frac{dn(n+1)}{2}$ (when $d\ge 2$ is even) or $(d+1)$ (when $d\ge 3$ is odd) distinct closed geodesics, or there exist infinitely many distinct closed geodesics.

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Huagui Duan, Dong Xie. 2022-01-26. Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics. https://arxiv.org/abs/2201.10975

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