Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913206880960512 |
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| author | Duan, Huagui Liu, Hui Long, Yiming Qi, Zihao Wang, Wei |
| author_facet | Duan, Huagui Liu, Hui Long, Yiming Qi, Zihao Wang, Wei |
| contents | In this paper, we prove that for every non-degenerate $C^3$ compact star-shaped hypersurface $Σ$ in $\mathbf{R}^{6}$ which carries no prime closed characteristic of Maslov-type index $0$ or no prime closed characteristic of Maslov-type index $-1$, there exist at least three prime closed characteristics on $Σ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$ Duan, Huagui Liu, Hui Long, Yiming Qi, Zihao Wang, Wei Dynamical Systems Symplectic Geometry In this paper, we prove that for every non-degenerate $C^3$ compact star-shaped hypersurface $Σ$ in $\mathbf{R}^{6}$ which carries no prime closed characteristic of Maslov-type index $0$ or no prime closed characteristic of Maslov-type index $-1$, there exist at least three prime closed characteristics on $Σ$. |
| title | Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$ |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2401.13259 |