# American Institute of Mathematical Sciences

September  2016, 36(9): 5131-5162. doi: 10.3934/dcds.2016023

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

 1 Department of Mathematics, University of Toronto, 40 St. George St., Room 6290, Toronto, Ontario, M5S 2E4, Canada

Received  July 2015 Revised  November 2015 Published  May 2016

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.
Citation: Guowei Yu. Periodic solutions of the planar N-center problem with topological constraints. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 5131-5162. doi: 10.3934/dcds.2016023
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