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arXiv · 1808.07633

Exponential stability of Euler integral in the three--body problem

Gabriella Pinzari
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Abstract

The first integral characteristic of the two--centres problem is proven to be an approximate integral (in the sense of N.N.Nekhorossev) to the three--body problem, at least if the masses are very different and the particles are constrained on the same plane. The proof uses a new normal form result, carefully designed around the degeneracies of the problem, and a new study of the phase portrait of the unperturbed problem. Applications to the prediction of collisions between the two minor bodies are shown.

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Gabriella Pinzari. 2018-08-23. Exponential stability of Euler integral in the three--body problem. https://arxiv.org/abs/1808.07633

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