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

Guowei Yu | Zendy

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

Author(s) -

Guowei Yu

Publication year - 2016

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2016023

Subject(s) - homotopy , center (category theory) , planar , mathematics , class (philosophy) , topology (electrical circuits) , pure mathematics , space (punctuation) , mathematical analysis , combinatorics , computer science , chemistry , computer graphics (images) , crystallography , artificial intelligence , operating system

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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