A Class Of Quasi Analytic Systems Center And The Isochronous Center

This thesis is devoted to the problems of the center conditions, and the isochronous conditions for quasi analytic systems. It is composed of two chapters.In chapter1, the historical background and the present progress of problem about center conditions, and the isochronous conditions of planar polynomial differential system were introduced and summarized.In chapter2, center condition and isochronous center of quasi fifth system were investigated. By converting quasi analysis system into complex system, the recursion formula for computation of singular point quantities were given, and with computer algebra system Mathematica, the first18singular point quantities were deduced, so the necessary and sufficient conditions for origin to be a center were obtained. Then on the basis of center conditions, with the computation of period constants, the necessary conditions for center to be an isochronous center were given, at the same time, proofs of isochronous center these system by using some effective methods were given. So far, the study of isochronous center of quasi analysis systems is a new field.