Transversal homoclinic orbits in the collinear restricted three-body problem. (English) Zbl 1094.70006
Summary: Using the Melnikov perturbation method, we prove the existence of transversal homoclinic points in the collinear restricted three-body problem. As a consequence, we can embed a Bernoulli shift in a suitable cross-section of the flow, showing that this problem possesses chaotic dynamics.
MSC:
70F07 | Three-body problems |
70K44 | Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics |
70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |