Symplectic Dynamics Working Group

We consider the elliptic restricted three-body problem as a perturbation of the circular problem, with the perturbation parameter being the eccentricity of the orbits of the primaries. We show that for every suitably small, non-zero perturbation parameter, there exist a set of initial conditions whose corresponding orbits make chaotic jumps in energy. The distributions of energies along these orbits converge to a Brownian motion with drift as the perturbation parameter tends to zero. We can obtain any desired values of the drift and of the variance for the limiting Brownian motion by choosing appropriate sets of initial conditions. Our results address a conjecture made by Chirikov. This is joint work with Maciej Capinski.