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

We classify the global phase portraits in the Poincaré disc of thedifferential systems $\dot{x}=-y+xf(x,y),$ $\dot{y}=x+yf(x,y)$,where $f(x,y)$ is a homogeneous polynomial of degree 3. Thesesystems have a uniform isochronous center at the origin. This papertogether with the results presented in [9] completes theclassification of the global phase portraits in the Poincaré disc ofall quartic polynomial differential systems with a uniformisochronous center at the origin.