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Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP

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Abstract

We consider the planar restricted three-body problem and the collinear equilibrium point L 3, as an example of a center × saddle equilibrium point in a Hamiltonian with two degrees of freedom. We explore numerically the existence of symmetric and non-symmetric homoclinic orbits to L 3, when varying the mass parameter μ. Concerning the symmetric homoclinic orbits (SHO), we study the multi-round, m-round, SHO for m ≥ 2. More precisely, given a transversal value of μ for which there is a 1-round SHO, say μ 1, we show that for any m ≥ 2, there are countable sets of values of μ, tending to μ 1, corresponding to m-round SHO. Some comments on related analytical results are also made.

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Authors and Affiliations

  1. Departament d’Informàtica i Matemàtica Aplicada, Universitat de Girona, Avda. Lluís Santaló s/n, 17071, Girona, Spain

    E. Barrabés

  2. IEEC and Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra, Spain

    J. M. Mondelo

  3. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028, Barcelona, Spain

    M. Ollé

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  1. E. Barrabés
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  2. J. M. Mondelo
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  3. M. Ollé
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Correspondence to E. Barrabés.

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Barrabés, E., Mondelo, J.M. & Ollé, M. Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP. Celest Mech Dyn Astr 105, 197–210 (2009). https://doi.org/10.1007/s10569-009-9190-9

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  • DOI: https://doi.org/10.1007/s10569-009-9190-9

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