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A note on a conjecture of Poincaré

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Abstract

We prove the following weakened version of Poincaré's conjecture on the density of periodic orbits of the restricted three-body problem: The measure of Lebesgue of the set of bounded orbits which are not contained in the closure of the set of periodic orbits goes to zero when the mass parameter does.

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Authors and Affiliations

  1. Secció de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, Spain

    Gerard Gómez & Jaume Llibre

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  1. Gerard Gómez
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  2. Jaume Llibre
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Gómez, G., Llibre, J. A note on a conjecture of Poincaré. Celestial Mechanics 24, 335–343 (1981). https://doi.org/10.1007/BF01230393

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  • DOI: https://doi.org/10.1007/BF01230393

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