The European Physical Journal Special Topics

, Volume 225, Issue 13–14, pp 2741–2750 | Cite as

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

Regular Article Hamiltonian Systems
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Part of the following topical collections:
  1. Temporal and Spatio-Temporal Dynamic Instabilities: Novel Computational and Experimental Approaches

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 ℤn-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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© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Matemáticas y Mecánica, IIMAS, Universidad Nacional Autónoma de MéxicoMéxico D.F.Mexico
  2. 2.Department of Computer ScienceConcordia UniversityMontréalCanada
  3. 3.Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México04510 México DFMexico

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