Classification of the centers and isochronous centers for a class of quartic-like systems

In this paper we classify the centers and isochronous centers for a class of polynomial differential systems in R2R2 of degree dd that in complex notation z=x+iy can be written as ż=iz+(zz¯)d−42(Az3z¯+Bz2z¯2+Cz¯4), where d≥4d≥4 is an arbitrary even positive integer and A,B,C∈CA,B,C∈C. Note that if d=4d=4 we obtain a special case of quartic polynomial differential systems which can have a center at the origin.