Arnold diffusion and oscillatory solutions in the planar three-body problem

Abstract

In this paper, the following results concerning the Newtonian three-body problem are obtained: (1) Arnold diffusion exists in the planar three-body problem, as conjectured by V. 1. Arnold (1964, Dokl. Acad. Nauk SSSR156, 9). (2) The Oscillatory solutions as well as capture and escaping solutions, among other classes of chaotic solutions, exist in the three-body problem. (3) A special and interesting phenomenon, which we call the pseudo Arnold diffusion, arises near infinity in the three-body problem. (4) As a result of the existence of Arnold diffusion, the planar three-body problem is non-integrable and there are no additional real analytic integrals besides the known ones. © 1994 Academic Press.