A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in ${\mathbf{R}}^{2n}$

Huagui Duan, Hui Liu, Wenyan Ren

In this paper, we prove that if all closed characteristics on a compact non-degenerate star-shaped hypersurface $\Sigma$ in ${\mathbf{R}}^{2n}$ are elliptic, then either there exist exact…