We study the effect of time-dependent, non-conservative perturbations on the dynamics along homoclinic orbits to a normally hyperbolic invariant manifold. We assume that the unperturbed system is Hamiltonian, and the normally hyperbolic invariant manifold is parametrized via action-angle coordinates. The homoclinic excursions can be described via the scattering map, which gives the future asymptotic of an orbit as a function of its past asymptotic. We provide explicit formulas, in terms of convergent integrals, for the perturbed scattering map expressed in action-angle coordinates. We illustrate these formulas for perturbations of both uncoupled and coupled rotator-pendulum systems.

我们研究了时间依赖的，非保守的扰动对沿同宿轨道到正常双曲不变流形的动力学的影响。我们假设无扰动系统是哈密顿量，并且通常双曲不变流形是通过作用角坐标进行参数化的。可以通过散射图来描述同宿漂移，该图给出了轨道未来的渐近性，作为其过去渐近的函数。我们以收敛积分的形式，为以动作角坐标表示的扰动散射图提供了明确的公式。我们举例说明了未耦合和耦合旋转摆系统的摄动公式。