A class of ninth degree system with four isochronous centers

In this paper we study a class of ninth degree system and obtain the conditions that its four singular points can be general centers and isochronous centers (or linearizable centers) at the same time by computing carefully and strict proof. What is worth mentioning is that the expressions of Liapunov constants and periodic constants are simpler, and recursive formulas of node point values are given for the first time, which is a new effective criterion for verifying isochronous centers.