https://doi.org/10.1140/epjst/e2016-60009-y
Regular Article
Symmetry-breaking for a restricted n-body problem in the Maxwell-ring configuration
1 Matemáticas y Mecánica, IIMAS, Universidad Nacional Autónoma de México, Admon. No. 20, Delegación Alvaro Obregón, 01000 México D.F., Mexico
2 Department of Computer Science, Concordia University, 1455 boulevard de Maisonneuve O., Montréal, Québec H3G 1M8, Canada
3 Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México DF, Mexico
a e-mail: calleja@mym.iimas.unam.mx
b e-mail: doedel@cs.concordia.ca
c e-mail: cgazpe@ciencias.unam.mx
Received: 21 January 2016
Revised: 15 June 2016
Published online: 22 November 2016
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.
© EDP Sciences, Springer-Verlag, 2016
