Wisdom system: dynamics in the adiabatic approximation (Q1766266)

The authors consider the elliptic planar restricted three-body problem (Sun-Jupiter-asteroid). It is shown that in the leading approximation the Hamiltonian of the problem, averaged over the asteroid and Jupiter mean longitudes near the resonance 3/1, possesses a rather simple structure. Namely, `fast' and `slow' phase variables emerge and, at fixed value of the 'slow' variables, the Hamiltonian becomes identical to that of the mathematical pendulum. This allows the authors to study the qualitative properties of solutions depending on the energy levels. Particularly, in the region of adiabatic chaos they find numerous stable periodic trajectories.