Periodic perturbations of central force problems and an application to a restricted $3$-body problem

Alberto Boscaggin, Walter Dambrosio, Guglielmo Feltrin

We consider a perturbation of a central force problem of the form \begin{equation*} \ddot x = V'(|x|) \frac{x}{|x|} + \varepsilon \,\nabla_x U(t,x), \quad x \in \mathbb{R}^{2} \set…