Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities

We classify the global phase portraits in the Poincaré disc of the differential systems x• = -y + xf(x; y); y• = x + yf(x; y), where f(x; y) is a ho-mogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in [9] com-pletes the classification of the global phase portraits in the Poincaré disc of all quartic polynomial differential systems with a uniform isochronous center at the origin.