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Motions close to escapes in the rhomboidal four body problem

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Abstract

In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analysis, we show certain transversal intersections of the invariant manifolds of parabolic orbits. We then introduce Symbolic Dynamics when the mass ratio is small, and when it is close to one. In the first case the escapes or captures predominate in the direction of one of the diagonals of the rhombus, while in the second case we find solutions escaping or being captured in the direction of both possible diagonals.

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Authors and Affiliations

  1. Departmento de Matemáticas, Universidad Autónoma Metropolitana, Iztapalapa, Apartado postal 55-532, Código Postal 09340, Mexico, D.F.

    Ernesto A. Lacomba & Ernesto Pérez-Chavela

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  1. Ernesto A. Lacomba
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  2. Ernesto Pérez-Chavela
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Lacomba, E.A., Pérez-Chavela, E. Motions close to escapes in the rhomboidal four body problem. Celestial Mech Dyn Astr 57, 411–437 (1993). https://doi.org/10.1007/BF00695713

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  • DOI: https://doi.org/10.1007/BF00695713

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