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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
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