一类四次多项式Poincare型系统原点为中心的若干条件

ON SEVERAI CONDITIONS FOR CETRE FOR A CLASS OF QUARATIC POLYNOMIALS POINCARE SYSTEM

本文讨论形为(?)=-y十XF_3(X·y)(?)=X+yF_3(X·y)的系统(其中F_3(X·y)为缺一次项的三次多项式)的中心焦点判定,在运用计算焦点量的一类新的递推式得出了此系统的前几个焦点量的基础上,得到了原点为此系统中心的几个条件.

In this paper, we consider system of tke formx=梱 + xF3(x, y)y = x + yF3(x, y)Ceatre-focus decision problem, (in which F3(x, y)is a polynomial of degree3 begiaig with terms of degre greater than 1 ). After using a class of inductive formulate for computing tke focul values to comput focul values up to six orders, we obtain several condition for center.