Transition Tori in the Planar Restricted Elliptic Three Body Problem
Dynamical Systems
2015-03-13 v2
Abstract
We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2, a Cantor set of Lyapounov orbits survives the perturbation. The orbits are perturbed to quasi-periodic invariant tori. We show that for a certain family of masses of the primaries, for such tori we have transversal intersections of stable and unstable manifolds, which lead to chaotic dynamics involving diffusion over a short range of energy levels. Some parts of our argument are nonrigorous, but are strongly backed by numerical computations.
Cite
@article{arxiv.0906.4896,
title = {Transition Tori in the Planar Restricted Elliptic Three Body Problem},
author = {Maciej J. Capinski and Piotr Zgliczynski},
journal= {arXiv preprint arXiv:0906.4896},
year = {2015}
}