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
Location: MSRI: Simons Auditorium
Three--body problem; Normal form theory; Two--centre problem; Euler Integral; Prediction of collisions; Canonical coordinates.
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.