|Location:||MSRI: Simons Auditorium|
In this talk we will present some results and some work in progress
about possible asymptotic motions in the planar three body problem.
Since Chazy (1922), it is known that the possible states that a 3BP
can approach as time tends to infinity are Hyperbolic, Parabolic, Bounded, and Oscillatory.
Hyperbolic and parabolic correspond to unbounded motion, but oscillatory
correspond to solutions where one of the bodies approaches the other two and then "goes again far away" once and again, therefore the limsup of this relative motion is infinite but its liminf is finite.
In this talk we will review some results where we prove the existence of
such solutions in the restricted three body problem (circular and
elliptic) and we will show how to see that these motions also exist for
the 3BP for any masses of the bodies.
The proof requires to prove the transversal intersection of the stable
and unstable manifolds of periodic orbits at ``infinity'', and use techniques of Arnold diffusion.
This is a joint work with M. Guardia P. Martin. L. Sabbagh