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Transversal Homoclinic Orbits in the Collinear Restricted Three-Body Problem

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Abstract

Using the perturbation method of Melnikov, we prove in a simple way the existence of transversal homoclinic points in the collinear restricted three-body problem. As a consequence we can embed a Bernoulli shift on a suitable cross section of the flow, showing easily that this problem possesses chaotic dynamics.

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Authors and Affiliations

  1. Departament de Matematiques, Universitat Autonoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    J. Llibre

  2. Departamento de Matematicas, UAM-Iztapalapa, Apdo, Postal 55-534, 09340, Mexico D. F., Mexico

    E. Perez-Chavela

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  1. J. Llibre
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  2. E. Perez-Chavela
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Correspondence to J. Llibre or E. Perez-Chavela.

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Llibre, J., Perez-Chavela, E. Transversal Homoclinic Orbits in the Collinear Restricted Three-Body Problem. J Nonlinear Sci 15, 1–10 (2005). https://doi.org/10.1007/s00332-004-0511-6

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  • DOI: https://doi.org/10.1007/s00332-004-0511-6

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