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Periodic solutions of the planar N-center problem with topological constraints

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  • In the planar $N$-center problem, given a non-trivial free homotopy class of the configuration space satisfying certain conditions, we show that there is at least one collision-free $T$-periodic solution for any positive $T.$ The direct method of calculus of variations is used and the main difficulty is to show that minimizers under certain topological constraints are free of collision.
    Mathematics Subject Classification: Primary: 70F10, 37N05.


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