Abstract
In this paper, we construct a certain planar four-body problem which exhibits fast energy growth under certain assumption. 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 L1 and L2 Lagrangian points and their heteroclinic intersections. Our model is the first known example in celestial mechanics about the a priori chaotic case of Arnold diffusion (Delshams et al 2006 Memoirs of the AMS vol 179).
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