Periodic solutions and regularization of a Kepler problem with time-dependent perturbation
Classical Analysis and ODEs
2020-01-15 v1 Dynamical Systems
Abstract
We consider a Kepler problem in dimension two or three, with a time-dependent -periodic perturbation. We prove that for any prescribed positive integer , there exist at least periodic solutions (with period ) as long as the perturbation is small enough. Here the solutions are understood in a general sense as they can have collisions. The concept of generalized solutions is defined intrinsically and it coincides with the notion obtained in Celestial Mechanics via the theory of regularization of collisions.
Cite
@article{arxiv.1710.08782,
title = {Periodic solutions and regularization of a Kepler problem with time-dependent perturbation},
author = {Alberto Boscaggin and Rafael Ortega and Lei Zhao},
journal= {arXiv preprint arXiv:1710.08782},
year = {2020}
}