2026/07/17 by Huagui Duan, Zihao Qi · 1 voice
#math.SG #math.DS
This paper focuses on the stability of a closed characteristic and invariant sets on star shaped hypersurfaces in \bf R2n with finitely many 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 or not locally maximal under dynamical convexity.