Mass dependence of the Kolmogorov—Arnold—Moser stability and low-order resonances in the kinetically coupled two-degree-of-freedom morse system

Abstract

The dependence on the mass ratio of the stability of Kolmogorov—Arnold—Moser surfaces around the central fixed point is numerically analyzed for the escape energy region in the kinetically coupled symmetric Morse system with two degrees of freedom. Strong third-order resonances, together with other weak resonances of higher order, are found for the approximate mass ratio δ = (1 + γ) −1 = 0.263 at the dissociation threshold E = 1.0 (in units of the dissociation energy) and for δ = 0.293 at E = 0.7, an approximate lowest energy for a globally widespread chaos to develop.