Isochronicity conditions for some planar polynomial systems

Abstract

We 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 Lienard type equation. Using the so-called C-algorithm we have found 27 new multiparameter isochronous centers.

31 pages