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We investigate the motion of a massless body interacting with the Maxwellrelative equilibrium, which consists of n bodies of equal mass at the verticesof a regular polygon that rotates around a central mass. The massless body hasthree equilibrium Zn-orbits from which families of Lyapunov orbits emerge.Numerical continuation of these families using a boundary value formulation isused to construct the bifurcation diagram for the case n=7, also including somesecondary and tertiary bifurcating families. We observe symmetry-breakingbifurcations in this system, as well as certain period-doubling bifurcations.

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