  This paper focuses on isochronicity of linear center perturbed by a
polynomial. Isochronicity of a linear center perturbed by a degree four and
degree five polynomials is studied, several new isochronous centers are found.
For homogeneous isochronous perturbations, a first integral and a linearizing
change of coordinates are presented. Moreover, a family of Abel polynomial
systems is also considered. By investigations until degree 10 we prove the
existence of a unique isochronous center. These results are established using a
computer implementation based on Urabe theorem.
