Escape dynamics in collinear atomic-like three mass point systems

TL;DR

This paper investigates escape mechanisms in collinear three-mass systems with specific interactions, showing most orbits lead to binary escape at zero energy and positive measure escape at positive energies, with numerical evidence of periodic orbits.

Contribution

It provides a detailed analysis of escape dynamics in collinear three-mass systems, including measure-theoretic results and numerical evidence of periodic orbits.

Findings

Most zero-energy orbits lead to binary escape configurations.

The set of initial conditions leading to full escape has zero measure at zero energy.

At positive energies, the full escape set has positive measure.

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 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