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arXiv · 2409.04460

Four closed characteristics on compact star-shaped hypersurfaces in $\mathbb{R}^{8}$

Huagui Duan·Dong Xie
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Abstract

In this paper, we proved that for every non-degenerate $C^3$ compact star-shaped hypersurface $\Sigma$ in $\mathbb{R}^{8}$ which carries no prime closed characteristic of Maslov-type index $-1$, there exist at least four prime closed characteristics on $\Sigma$.

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Huagui Duan, Dong Xie. 2024-09-02. Four closed characteristics on compact star-shaped hypersurfaces in $\mathbb{R}^{8}$. https://arxiv.org/abs/2409.04460

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