Symmetry-breaking for a restricted n-body problem in the Maxwell-ring configuration
arXiv:1601.06160 · doi:10.1140/epjst/e2016-60009-y
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.
10 pages, 7 figures