Stability of closed characteristics on symmetric compact convex hypersurfaces in ${\mathbb{R}}^{2n}$

Abstract

In this article, let $\Sigma \subset {\mathbb{R}}^{2n}$ be a compact convex hypersurface which is symmetric with respect to the origin. We prove that if $\Sg$ carries finitely many geometrically distinct closed characteristics, then at least $n-1$ of them must be non-hyperbolic; if $\Sg$ carries exactly $n$ geometrically distinct closed characteristics, then at least two of them must be elliptic.

18 pages

References in corpus (2)

• Index iteration theory for symplectic paths with applications to nonlinear Hamiltonian systems
• Stability of closed characteristics on compact convex hypersurfaces in ${\mathbb{R}}^6$

Cited by in corpus (1)

• Stability of closed characteristics on compact hypersurfaces in ${\mathbb{R}}^{2n}$ under pinching condition