Limit Cycles and Isochronous Centers in a Class of Ninth Degree System

Abstract

A class of ninth degree system is studied and the conditions ensuring that its five singular points can be centers and isochronous centers (or linearizable centers) at the same time by exact calculation and strict proof are obtained. What is more, the expressions of Lyapunov constants and periodic constants are simplified, and 21 limit circles could be bifurcated at least.