Abstract:We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless particle on the z-axis. The study of the motion of this particle can then be modeled as a timedependent Hamiltonian System. We give a geometric construction of a surface in the three-dimensional phase space separating orbits for which the massless particle escapes to infinit… Show more
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