Escape dynamics in collinear atomic-like three mass point systems

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 systems with non-negative total energy. We show that on the zero energy level set, most of the orbits lead to binary escape configurations and the set of initial conditions leading to escape configurations where all three separations infinitely increase as $t \to \infty 1$ has zero Lebesgue measure. We also give numerical evidence of the existence of a periodic orbit for the case when the two outer masses are equal. For positive energies, we prove that the set of initial conditions leading to escape configurations where all three separations infinitely increase as $t \to \infty$ has positive Lebesgue measure. Keywords: linear three point