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

Hamiltonian systems, from topology to applications through analysis I October 08, 2018 - October 12, 2018

October 11, 2018 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Gabriella Pinzari (University of Padova)
Location: MSRI: Simons Auditorium
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The first integral characteristic of the fixed two--centre 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 a 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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