## Taiwanese Journal of Mathematics

- Taiwanese J. Math.
- Volume 21, Number 6 (2017), 1437-1453.

### Extensions to Chen's Minimizing Equal Mass Parallelogram Solutions

Abdalla Mansur, Daniel Offin, and Alessandro Arsie

#### Abstract

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.

#### Article information

**Source**

Taiwanese J. Math., Volume 21, Number 6 (2017), 1437-1453.

**Dates**

Received: 1 July 2017

Revised: 9 October 2017

Accepted: 22 October 2017

First available in Project Euclid: 26 October 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.twjm/1508983228

**Digital Object Identifier**

doi:10.11650/tjm/171003

**Mathematical Reviews number (MathSciNet)**

MR3732913

**Zentralblatt MATH identifier**

06871376

**Subjects**

Primary: 34C35 34C27: Almost and pseudo-almost periodic solutions 54H20: Topological dynamics [See also 28Dxx, 37Bxx]

**Keywords**

Hamiltonian $n$-body problem equivariant action integral

#### Citation

Mansur, Abdalla; Offin, Daniel; Arsie, Alessandro. Extensions to Chen's Minimizing Equal Mass Parallelogram Solutions. Taiwanese J. Math. 21 (2017), no. 6, 1437--1453. doi:10.11650/tjm/171003. https://projecteuclid.org/euclid.twjm/1508983228