Escape dynamics in collinear atomic-like three mass point systems

Abstract

The present paper studies the escape mechanism in collinear three point mass systems with small-range-repulsive/large-range-attractive pairwise interaction. Specifically, we focus on the asymptotic behaviour for systems with non-negative total energy. On the zero energy level set there are two distinct asymptotic states, called 1 + 1 + 1 escape configurations, where all the three separations infinitely increase as t → ∞ . We show that 1 + 1 + 1 escapes are improbable by proving that the set of initial conditions leading to such asymptotic configurations has zero Lebesgue measure. When the outer mass points are of the same kind we deduce the existence of a heteroclinic orbit connecting the 1 + 1 + 1 escape configurations. We further prove that this orbit is stable under parameter perturbation. In the positive energies’ case, we show that the set of initial conditions leading to 1 + 1 + 1 escape configurations has positive Lebesgue measure.