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Abstract and Applied Analysis
Volume 2012, Article ID 783546, 24 pages
http://dx.doi.org/10.1155/2012/783546
Research Article

Integrability and Pseudo-Linearizable Conditions in a Quasi-Analytic System

1School of Mathematical Science and Computing Technology, Central South University, Hunan, Changsha 410075, China
2School of Mathematics and Statistics, Henan University of Science and Technology, Henan, Luoyang 471003, China

Received 30 October 2011; Revised 27 November 2011; Accepted 13 January 2012

Academic Editor: P. J. Y. Wong

Copyright © 2012 Feng Li and Yusen Wu. 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

This paper deals with the problems of integrability and linearizable conditions at degenerate singular point in a class of quasianalytic septic polynomial differential system. We solve the problems by an indirect method, that is, we transform the quasianalytic system into an analytic system firstly, and the degenerate singular point into an elementary singular point. Then we calculate the singular values at the origin of the analytic system by the known classical methods. We obtain the center conditions and isochronous center conditions. Accordingly, integrability and pseudolinearizable conditions at degenerate singular point in the quasianalytic system are obtained. Especially, when 𝜆 = 1 , the system has been studied in Wu and Zhang (2010).