Chaotic Diffusion in Celestial Mechanics

Among the spectacular results of modern celestial mechanics, the discovery of chaotic diffusion of eccentricities and inclination is probably the most interesting aspect for the broader community interested in general chaos theory. Indeed it reveals a mechanism that should be generic in moderate order resonances among the fast degrees of freedom of any degenerate Hamiltonian system. This paper discusses the resonant structure that is at the base of this chaotic diffusion process and illustrates an approximated method to estimate the diffusion timescale. Examples on the relevance of chaotic diffusion for the dynamics of small bodies of the solar system are also provided.