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December, 2017 Extensions to Chen's Minimizing Equal Mass Parallelogram Solutions
Abdalla Mansur, Daniel Offin, Alessandro Arsie
Taiwanese J. Math. 21(6): 1437-1453 (December, 2017). DOI: 10.11650/tjm/171003


In this paper, we study the extension of the minimizing equal mass parallelogram solutions which was derived by Chen in 2001 [2]. Chen's solution was minimizing for one quarter of the period $[0,T]$, where numerical integration had been used in his proof. In this paper we extend Chen's solution in the reduced space to $[0,4T]$ and we show that this extension is also minimizing over the intervals $[0,2T]$ and $[0,4T]$. The minimizing property of the extension is proved without using numerical integration.


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Abdalla Mansur. Daniel Offin. Alessandro Arsie. "Extensions to Chen's Minimizing Equal Mass Parallelogram Solutions." Taiwanese J. Math. 21 (6) 1437 - 1453, December, 2017.


Received: 1 July 2017; Revised: 9 October 2017; Accepted: 22 October 2017; Published: December, 2017
First available in Project Euclid: 26 October 2017

zbMATH: 06871376
MathSciNet: MR3732913
Digital Object Identifier: 10.11650/tjm/171003

Primary: 34C27 , 34C35 , 54H20‎

Keywords: $n$-body problem , equivariant action integral , Hamiltonian

Rights: Copyright © 2017 The Mathematical Society of the Republic of China


Vol.21 • No. 6 • December, 2017
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