Journal of Applied Mathematics
Volume 2011 (2011), Article ID 762762, 18 pages
http://dx.doi.org/10.1155/2011/762762
Research Article

Sufficient and Necessary Center Conditions for the Poincaré Systems 𝑃 ( 2 , 2 𝑛 ) ( 𝑛 ≤ 5 )

Jinya Xu1 and Zhengyi Lu1,2

1Institute of Computer Applications, Academia Sinica, Chengdu 610041, China
2Department of Mathematics, Sichuan Normal University, Chengdu 610068, China

Received 22 August 2011; Revised 27 October 2011; Accepted 28 October 2011

Academic Editor: Mohamad Alwash

Copyright © 2011 Jinya Xu and Zhengyi Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain sufficient and necessary center conditions for the Poincaré system 𝑃 ( 2 , 2 𝑛 ) ( 𝑛 ≤ 5 ) . The necessity of the condition is derived from the first 2 𝑛 focal values by symbolic computation with Maple, and the sufficiency is proved by Volokitin's method.