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arXiv · 2607.15546

Stability of closed characteristics and invariant sets on star-shaped hypersurfaces

Huagui Duan·Zihao Qi
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Abstract

This paper focuses on the stability of a closed characteristic and invariant sets on compact star shaped hypersurfaces in ${\bf R}^{2n}$ with finitely many simple closed characteristics. Firstly, it is proved that all closed characteristics are non-hyperbolic, under some index condition weaker than dynamical convexity. Secondly, when $n=3$, it is proved that all closed characteristics are elliptic when their number is exactly $3$, under non-degeneracy and some minor index condition. Lastly, it is proved that all closed characteristics are either degenerate at some iteration or not locally maximal under dynamical convexity.

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Huagui Duan, Zihao Qi. 2026-07-17. Stability of closed characteristics and invariant sets on star-shaped hypersurfaces. https://arxiv.org/abs/2607.15546

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