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

¹ Dalian University of Technology, School of Mathematical Sciences, Dalian District of Ganjingzi City Road 2, 116024, China
² Università degli Studi di Padova, Dipartimento di Matematica, Via Trieste 63, 35121 Padova, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 December 2025
Accepted: 17 April 2026

Abstract

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.