| Résume | Consider the Restricted Planar Elliptic Three Body Problem. This problem models the Sun-Jupiter-Asteroid dynamics. For eccentricity of Jupiter $e_0$ small enough, we show that there exists a family of probability measures supported at the $3 : 1$ mean motion resonance such that the push forward under the associated Hamiltonian flow has the following property. At the timescale $te_0^{-2}$, the distribution of the Jacobi constant of the Asteroid weakly converges to an Ito diffusion process on the line as $e_0\to 0$. This resonance corresponds to the biggest of the Kirkwood gap on the Asteroid belt in the Solar System. This is a joint work with V. Kaloshin, P. Martin and P. Roldan. |
