A general method is presented for constructing a nonlinear canonical transformation, which makes it possible to introduce local variables in a neighborhood of periodic motions of an autonomous Hamiltonian system with two degrees of freedom. This method can be used for investigating the behavior of the Hamiltonian system in the vicinity of its periodic trajectories. In particular, it can be applied to solve the problem of orbital stability of periodic motions.

中文翻译：

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二自由度哈密顿系统周期解邻域引入局部变量的方法

提出了一种构造非线性正则变换的通用方法，该方法使得在具有两个自由度的自治哈密顿系统的周期运动邻域中引入局部变量成为可能。该方法可用于研究哈密顿系统在其周期轨迹附近的行为。特别是可以应用于解决周期运动的轨道稳定性问题。