Heteroclinic connections between triple collisions and relative periodic orbits in the isosceles three-body problem

Abstract

We study the isosceles three-body problem and show that there exist infinitely many families of relative periodic orbits converging to heteroclinic cycles between equilibria on the collision manifold in Devaney's blown-up coordinates. Towards this end, we prove that two types of heteroclinic orbits exist in much wider parameter ranges than previously detected, using self-validating interval arithmetic calculations, and we appeal to the previous results on heteroclinic orbits. Moreover, we give numerical computations for heteroclinic and relative periodic orbits to demonstrate our theoretical results. The numerical results also indicate that the two types of heteroclinic orbits and families of relative periodic orbits exist in wider parameter regions than detected in the theory and that some of them are related to Euler orbits.