Seminar

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