Isochronicity conditions for some planar polynomial systems II

We study the isochronicity of centers at O∈R2 for systemsx˙=−y+A(x,y),y˙=x+B(x,y), where A,B∈R[x,y], which can be reduced to the Liénard type equation. When deg(A)⩽4 and deg(B)⩽4, using the so-called C-algorithm we found 36 new multiparameter families of isochronous centers. For a large class of isochronous centers we provide an explicit general formula for linearization. This paper is a direct continuation of a previous one with the same title [Islam Boussaada, A. Raouf Chouikha, Jean-Marie Strelcyn, Isochronicity conditions for some planar polynomial systems, Bull. Sci. Math. 135 (1) (2011) 89-112], but it can be read independently.