Closed trajectories on symmetric convex Hamiltonian energy surfaces

Abstract

In this article, let $\Sigma \subset {\mathbb{R}}^{2n}$ be a compact convex Hamiltonian energy surface which is symmetric with respect to the origin. where $n\ge 2$. We prove that there exist at least two geometrically distinct symmetric closed trajectories of the Reeb vector field on $\Sg$.

27pages

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 ${\mathbb{R}}^6$