Computing center conditions for resonant infinity via integrating factor method

In this literature, the calculation of generalized center conditions is addressed for resonant infinity of a polynomial vector field in C². The technique is taking resonant infinity into elementary resonant origin by a homeomorphism. Afterwards, an algorithm to compute generalized singular point quantities is developed, which is a good approach to find the necessary conditions of generalized center for any rational resonance ratio. Finally, the necessary and sufficient conditions of generalized center for resonant infinity are obtained.