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Volume 18, Issue 4

Existence of Prograde Double-Double Orbits in the Equal-Mass Four-Body Problem

Wentian Kuang
/ Duokui Yan
Published Online: 2018-03-08 | DOI: https://doi.org/10.1515/ans-2018-0009

Abstract

By introducing simple topological constraints and applying a binary decomposition method, we show the existence of a set of prograde double-double orbits for any rotation angle $\theta \in \left(0,\pi /7\right]$ in the equal-mass four-body problem. A new geometric argument is introduced to show that for any $\theta \in \left(0,\pi /2\right)$, the action of the minimizer corresponding to the prograde double-double orbit is strictly greater than the action of the minimizer corresponding to the retrograde double-double orbit. This geometric argument can also be applied to study orbits in the planar three-body problem, such as the retrograde orbits, the prograde orbits, the Schubart orbit and the Hénon orbit.

MSC 2010: 70F10; 70F16; 70F07

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Revised: 2018-02-01

Published Online: 2018-03-08

Published in Print: 2018-11-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11131004

Award identifier / Grant number: 11671215

Award identifier / Grant number: 11432001

The first author was partially supported by the Ph.D. Candidate Research Innovation Fund of Nankai University and NSFC (no. 11131004 and 11671215). The second author was supported by NSFC (no. 11432001) and the China Scholarship Council.

Citation Information: Advanced Nonlinear Studies, Volume 18, Issue 4, Pages 819–843, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365,

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