Oscillatory motions in the restricted three body problem
speaker: Pau Martin (Dept. MAIV - Universitat Politecnica de Catalunya)abstract: The restricted three body problem is a simplified model of the three body problem where one of the bodies has zero mass and the other two, the primaries, evolve describing Keplerian ellipses. According to Chazy, there are only four possible final states in the movement of the zero mass body. One of them are oscillatory motions, that is, orbits that go closer and closer to infinity but always return to a fixed neighborhood of the primaries. Chazy knew examples all possible final states, except oscillatory ones.
The existence of such motions has been proved by several authors in different instances of the restricted three body problem, Sitnikov, Alexeev, Moser, Llibre and Sim\'{o} and Moeckel, among others.
In this work we prove that oscillatory motions do exist in the restricted planar circular three body problem for all values of the masses.
The proof is based on the computation of the splitting of the parabolic invariant manifolds of infinity.
timetable:
Thu 8 May, 16:00 - 17:00, Aula Dini
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