Conditions of infinity to be an isochronous centre for a rational differential system

In this article we find conditions under which infinity is a centre or an isochronous centre for a rational differential system. By a transformation, infinity is taken to the origin and therefore properties at infinity can be studied by using the methods developed for finite critical points. Using the computer algebra system—Mathematica we compute the singular point values and the period constants at the origin for the transformed system and then get the necessary conditions of the problems. Finally, we prove that the conditions are sufficient.