Oscillatory motions and Arnold diffusion in the restricted
planar three body problem
Tere M Seara
The restricted (elliptic) three body problem considers the motion of a
particle with zero mass under the effects of two bodies called primaries,
which move in elliptic orbits around their center of mass.
The circular case is a particular case of the elliptic case where the
primaries move in circular orbits.
The first part of this talk proves the existence of oscillatory motions
for the restricted planar circular three body problem, that is, we will
show that there exist orbits which leave every bounded region but which
return infinitely often to some fixed bounded region. Our work does not
need to assume any smallness about the mass ratio.
We show that, for large enough Jacobi constant, there exist transversal
intersections between the stable and unstable manifolds of infinity which
guarantee the existence of a symbolic dynamics that creates the so called
The main achievement is to rigorously prove the transversality of the
invariant manifolds without assuming the mass ratio small, since then this
transversality can not be checked by using classical perturbation theory
respect to the mass ratio.
The second part of the talk extends these results about the invariant
manifolds to the elliptic case, taking the mass ratio and the eccentricity
of the primaries small enough. As a consequence we obtain orbits of the
elliptic restricted three body problem whose angular momentum increases.
This behaviour is usually called Arnold diffusion.