We provide sufficient conditions on the four parameters of a Hamiltonian system, related with the Friedmann–Robertson–Walker Hamiltonian system in a rotating reference frame, which guarantee the existence of 12 continuous families of periodic orbits, parameterized by the values of the Hamiltonian, which born at the equilibrium point localized at the origin of coordinates. The main tool for finding analytically these families of periodic orbits is the averaging theory for computing periodic orbits adapted to the Hamiltonian systems. The technique here used can be applied to arbitrary Hamiltonian systems.

中文翻译：

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与旋转坐标系中的Friedmann–Robertson–Walker系统相关的哈密顿系统的周期轨道

我们在旋转参考系中为与Friedmann–Robertson–Walker哈密顿系统相关的哈密顿系统的四个参数提供了充分的条件，这些条件保证存在12个连续的周期性轨道族，并由哈密顿值来参数化，出生于位于坐标原点的平衡点。用于分析性地找到这些周期轨道族的主要工具是用于计算适用于哈密顿系统的周期轨道的平均理论。这里使用的技术可以应用于任意哈密顿系统。