Exponential stability in the perturbed central force problem
Mathematical Physics
2019-09-20 v3 math.MP
Abstract
We consider the spatial central force problem with a real analytic potential. We prove that for all analytic potentials, but the Keplerian and the Harmonic ones, the Hamiltonian fulfills a nondegeneracy property needed for the applicability of Nekhoroshev's theorem. We deduce stability of the actions over exponentially long times when the system is subject to arbitrary analytic perturbation. The case where the central system is put in interaction with a slow system is also studied and stability over exponentially long time is proved.
Cite
@article{arxiv.1705.00576,
title = {Exponential stability in the perturbed central force problem},
author = {Dario Bambusi and Alessandra Fusé and Marco Sansottera},
journal= {arXiv preprint arXiv:1705.00576},
year = {2019}
}
Comments
29 pages, 1 figure