Explorations of chaotic diffusions triggered by multiple close encounters in a mean motion resonance of the three-body problem

The motion of comets and asteroids for large values of their eccentricity may experience instabilities due to both the action of resonance induced chaos and close encounters with a planet. The spatial circular restricted three-body problem incorporates three characteristic timescales of the phenomenon: a very short one in which the dynamics is dominated by the close encounter with a planet, an intermediate one in which the dynamics is described by a resonant normal form, and a secular one characterized by possible long-term evolution of orbital elements. While extensive literature exists on normal form dynamics, long-term adiabatic evolution, and deep close encounters, less is known about chaotic instability resulting from the accumulation of a sequence of multiple weak close encounters. In this paper, using a combined analysis that leverages the computation of approximate first integrals, of Fast Lyapunov Indicators, of the localization of the gravitational singularities in the phase-space, and of adiabatic theory, we provide examples of chaotic diffusion that, in addition to the crossings of a separatrix, are due to the accumulation of effects of weak close encounters. In particular, we provide examples of how a deeper close encounter may determine the extraction from a main resonance, such as the 1:2 mean motion resonance with Neptune, and the subsequent cascade of close encounters determines a slower chaotic diffusion between the nearby resonances.