Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$

Huagui Duan; Hui Liu; Yiming Long; Zihao Qi; Wei Wang

Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$

Dynamical Systems 2024-01-25 v1 Symplectic Geometry

Authors: Huagui Duan , Hui Liu , Yiming Long , Zihao Qi , Wei Wang

Abstract

In this paper, we prove that for every non-degenerate $C^3$ compact star-shaped hypersurface $\Sigma$ 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 $\Sigma$ .

Keywords

closed characteristics non-degenerate star-shaped hypersurfaces Maslov-type index prime closed characteristics Hamiltonian dynamics

Cite

@article{arxiv.2401.13259,
  title  = {Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$},
  author = {Huagui Duan and Hui Liu and Yiming Long and Zihao Qi and Wei Wang},
  journal= {arXiv preprint arXiv:2401.13259},
  year   = {2024}
}

Comments

30 pages. arXiv admin note: text overlap with arXiv:2205.07082, arXiv:1510.08648, arXiv:2205.14789

Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$

Abstract

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