Periodic Solutions of the Planar N-Center Problem with topological constraints

Abstract

In the planar $N$-center problem, for a non-trivial free homotopy class of the configuration space satisfying certain mild condition, we show that there is at least one collision free $T$-periodic solution for any positive $T.$ We use the direct method of calculus of variations and the main difficulty is to show that minimizers under certain topological constraints are free of collision.

34 pages, 5 figures, major revision in section 4, minor revision in section 1

References in corpus (2)

• Entire minimal parabolic trajectories: the planar anisotropic Kepler problem
• Variational proof of the existence of the super-eight orbit in the four-body problem