Four closed characteristics on compact star-shaped hypersurfaces in $\mathbb{R}^{8}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914940904800256 |
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| author | Duan, Huagui Xie, Dong |
| author_facet | Duan, Huagui Xie, Dong |
| contents | In this paper, we proved that for every non-degenerate $C^3$ compact star-shaped hypersurface $Σ$ in $\mathbb{R}^{8}$ which carries no prime closed characteristic of Maslov-type index $-1$, there exist at least four prime closed characteristics on $Σ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Four closed characteristics on compact star-shaped hypersurfaces in $\mathbb{R}^{8}$ Duan, Huagui Xie, Dong Differential Geometry Dynamical Systems 58E05, 37J46, 34C25 In this paper, we proved that for every non-degenerate $C^3$ compact star-shaped hypersurface $Σ$ in $\mathbb{R}^{8}$ which carries no prime closed characteristic of Maslov-type index $-1$, there exist at least four prime closed characteristics on $Σ$. |
| title | Four closed characteristics on compact star-shaped hypersurfaces in $\mathbb{R}^{8}$ |
| topic | Differential Geometry Dynamical Systems 58E05, 37J46, 34C25 |
| url | https://arxiv.org/abs/2409.04460 |