Periodic solutions of symmetric Hamiltonian systems

Abstract

This paper is devoted to the study of periodic solutions of Hamiltonian system $\dot{z}(t)=J\nabla H(z(t))$, where $H$ is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a nearby of non-isolated critical points of $H$ which form orbits of the group action. We prove Lyapunov-type theorem for symmetric Hamiltonian systems.

22 pages. Arch Rational Mech Anal (2020)

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