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Symmetry-breaking for a restricted n-body problem in the Maxwell-ring configuration

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Abstract

We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that rotates around a central mass. The massless body has three equilibrium ℤ n -orbits from which families of Lyapunov orbits emerge. Numerical continuation of these families using a boundary value formulation is used to construct the bifurcation diagram for the case n = 7, also including some secondary and tertiary bifurcating families. We observe symmetry-breaking bifurcations in this system, as well as certain period-doubling bifurcations.

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Authors and Affiliations

  1. Matemáticas y Mecánica, IIMAS, Universidad Nacional Autónoma de México, Admon. No. 20, Delegación Alvaro Obregón, 01000, México D.F., Mexico

    Renato Calleja

  2. Department of Computer Science, Concordia University, 1455 boulevard de Maisonneuve O., Montréal, Québec H3G 1M8, Canada

    Eusebius Doedel

  3. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México DF, Mexico

    Carlos García-Azpeitia

Authors
  1. Renato Calleja
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  2. Eusebius Doedel
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  3. Carlos García-Azpeitia
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Corresponding authors

Correspondence to Renato Calleja, Eusebius Doedel or Carlos García-Azpeitia.

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Calleja, R., Doedel, E. & García-Azpeitia, C. Symmetry-breaking for a restricted n-body problem in the Maxwell-ring configuration. Eur. Phys. J. Spec. Top. 225, 2741–2750 (2016). https://doi.org/10.1140/epjst/e2016-60009-y

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  • DOI: https://doi.org/10.1140/epjst/e2016-60009-y

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