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Characterization of transversal homothetic solutions in the n-body problem

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Abstract

Homothetic solutions of the n-body problem can be seen as heteroclinic orbits when the dynamical variables are changed via the McGehee blow-up and the time is suitably scaled. Transversality of the invariant asymptotic manifolds which contain the heteroclinic orbits is related to some structural stability. We fully characterize the cases in which such transversality is obtained for the n-body problem in any dimension.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Spain

    Carles Simó & Jaume Llibre

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

    Carles Simó & Jaume Llibre

Authors
  1. Carles Simó
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  2. Jaume Llibre
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Communicated by C. Truesdell

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Simó, C., Llibre, J. Characterization of transversal homothetic solutions in the n-body problem. Arch. Rational Mech. Anal. 77, 189–198 (1981). https://doi.org/10.1007/BF00250623

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  • DOI: https://doi.org/10.1007/BF00250623

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