Stability of closed characteristics on compact convex hypersurfaces in ${\mathbb{R}}^6$

Abstract

In this paper, let $\Sigma \subset {\mathbb{R}}^6$ be a compact convex hypersurface. We prove that if $\Sigma$ carries only finitely many geometrically distinct closed characteristics, then at least two of them must possess irrational mean indices. Moreover, if $\Sg$ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.

24 pages, to appear in J. Eur. Math. Soc

Cited by in corpus (1)

• Closed trajectories on symmetric convex Hamiltonian energy surfaces