This 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.

中文翻译：

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对称哈密顿系统的周期解

本文致力于研究哈密顿系统的周期解 $$\dot{z}(t)=J \nabla H(z(t))$$ z ˙ ( t ) = J ∇ H ( z ( t ) ) ，其中 H 在紧李群作用下是对称的。我们正在寻找 H 的非孤立临界点附近的周期解，这些临界点形成群作用的轨道。我们证明了对称哈密顿系统的李雅普诺夫型定理。