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

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 $\lambda =1$, the system has been studied in Wu and Zhang (2010).