Abstract
AbstractThis paper is devoted to the study of periodic solutions of a Hamiltonian system $$\dot{z}(t)=J \nabla H(z(t))$$
z
˙
(
t
)
=
J
∇
H
(
z
(
t
)
)
, where H is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a neighborhood of non-isolated critical points of H which form orbits of the group action. We prove a Lyapunov-type theorem for symmetric Hamiltonian systems.
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mathematics (miscellaneous),Analysis
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