Isochronicity conditions for some planar polynomial systems II

International audienceWe study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $$\dot x=-y+A(x,y),\;\dot y=x+B(x,y),$$ where $A,\;B\in \mathbb{R}[x,y]$, which can be reduced to the Liénard type equation. When $deg(A)\leq 4$ and $deg(B) \leq 4$, using the so-called C-algorithm we found $36$ new families of isochronous centers. When the Urabe function $h=0$ we provide an explicit general formula for linearization. This paper is a direct continuation of [I. Boussaada, A.R. Chouikha, J-M. Strelcyn, Isochronicity conditions for some planar polynomial systems, To appear in Bulletins des Sciences Mathématiques, 2010] but can be read independantly