Closed trajectories on symmetric convex Hamiltonian energy surfaces

Details Closed trajectories on symmetric convex Hamiltonian energy surfaces Closed trajectories on symmetric convex Hamiltonian energy surfaces

2009-09-19

arxiv.org/abs/0909.3564v1

Mathematics

Symplectic Geometry

27pages

Scientific paper

In this article, let $\Sigma\subset\R^{2n}$ 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 $\Sg$.

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