Arnold Diffusion in a Restricted Planar Four-Body Problem

TL;DR

This paper demonstrates Arnold diffusion in a specially constructed four-body celestial system, showing fast energy growth through heteroclinic cycles, marking the first such example in celestial mechanics.

Contribution

It constructs a novel four-body problem model exhibiting Arnold diffusion, utilizing heteroclinic cycles and advanced mechanisms to demonstrate chaotic energy growth.

Findings

First example of Arnold diffusion in celestial mechanics

Constructs a four-body problem with fast energy growth

Uses heteroclinic cycles between Lyapunov orbits

Abstract

This paper constructs a certain planar four-body problem which exhibits fast energy growth. The system considered is a quasi-periodic perturbation of the Restricted Planar Circular three-body Problem (RPC3BP). Gelfreich-Turaev's and de la Llave's mechanism is employed to obtain the fast energy growth. The diffusion is created by a heteroclinic cycle formed by two Lyapunov periodic orbits surrounding $L_1$ and $L_2$ Lagrangian points and their heteroclinic intersections. Our model is the first known example in celestial mechanics of the a priori chaotic case of Arnold diffusion.