Closed trajectories on symmetric convex Hamiltonian energy surfaces

Abstract

In this article, let $\Sigma\subset\mathbf{R}^{2n}$ be a compactconvex Hamiltonian energy surface which is symmetric with respect tothe origin, where $n\ge 2$. We prove that there exist at least twogeometrically distinct symmetric closed trajectories of the Reebvector field on $\Sigma$.