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arXiv · 0906.4896

Transition Tori in the Planar Restricted Elliptic Three Body Problem

Maciej J. Capinski·Piotr Zgliczynski
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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.

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Maciej J. Capinski, Piotr Zgliczynski. 2009-06-26. Transition Tori in the Planar Restricted Elliptic Three Body Problem. https://arxiv.org/abs/0906.4896

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