以y^n=x^(n+1)-x^n为不变曲线的二次系统

The quadratic system with an invariant curve y^n=x^(n+1)-x^n

证明了以yn=xn+1-xn,n∈Z为不变曲线的二次系统当n≥3或n≤1时至多存在一个极限环,结合文[1]的结论,说明了以yn=xn+1-xn,n∈Z为不变曲线的二次系统至多有一个极限环.

It is proved that the quadratic system with an invariant curve yn=xn+1-xn,n∈Z has at most one limit cycle when n≥3 or n≤1,with the results in paper ,the system has at most one limit cycle for any n∈Z.