Instability in a Hamiltonian system and the distribution of asteroids

The formal stability of periodic solutions is investigated for a Hamiltonian system in two degrees of freedom. The nature of the zones of instability is exhibited in the case of a resonance of order $q\geqslant3$. In contrast to classical theory, an isoenergetic reduction is not carried out. This permits unstable solutions close to periodic solutions to be studied in full. The results are applied to the restricted problem of three bodies, which allows us to explain qualitatively the nature of all gaps with $q\geqslant3$ in the distribution of asteroids.
Figures: 19.
Bibliography: 37 titles.