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

Guowei Yu

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arXiv · 1507.02883

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

Guowei Yu

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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.

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Guowei Yu. 2015-07-10. Periodic Solutions of the Planar N-Center Problem with topological constraints. https://arxiv.org/abs/1507.02883

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