Tere M-Seara, Universitat Politècnica de Catalunya
Consider the planar 3 Body Problem with any masses, no all of them equal. In this talk we address two fundamental questions: the existence of oscillatory motions and of chaotic dynamics. In 1922, Chazy classified the possible final motions of the three bodies. One of the possible behaviours are oscillatory motions, that is, solutions of the 3 Body Problem such that the bodies leave every bounded region but which return infinitely often to some fixed bounded region. We prove that such motions exists. We also prove that one can construct solutions of the three body problem whose forward and backward final motions are of different type. This result relies on constructing invariant sets whose dynamics is conjugated to the (infinite symbols) Bernouilli shift. These sets are hyperbolic for the symplectically reduced planar 3 Body Problem. As a consequence, we obtain the existence of chaotic motions, an infinite number of periodic orbits and positive topological entropy for the 3 Body Problem.
This is a joint work with: Marcel Guardia, Pau Martin and Jaime Paradela.