Symmetric periodic orbits in three sub-problems of the $N$-body problem

Nai-Chia Chen

doi:10.3934/dcdsb.2014.19.1523

Article Contents

2014, Volume 19, Issue 6: 1523-1548. Doi: 10.3934/dcdsb.2014.19.1523

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Symmetric periodic orbits in three sub-problems of the $N$-body problem

Nai-Chia Chen^1,

1.
School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received: October 31, 2013

Revised: February 28, 2014

Published: July 2014

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Abstract

We study three sub-problems of the $N$-body problem that have two degrees of freedom, namely the $n-$pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of symmetric periodic orbits, including ``Schubart-like" orbits and brake orbits, by using topological shooting arguments.

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Mathematics Subject Classification: Primary: 70F07; Secondary: 37C27.

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