Transition Tori in the Planar Restricted Elliptic Three Body Problem

Details Transition Tori in the Planar Restricted Elliptic Three Body Problem Transition Tori in the Planar Restricted Elliptic Three Body Problem

2009-06-26

arxiv.org/abs/0906.4896v2

Mathematics

Dynamical Systems

Scientific paper

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.

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