Computing center conditions for non-analytic ninth degree vector fields with constant angular speed

摘要

We investigate the planar ninth degree non-analytic Poincare systems which have center-focus equilibriums at the origins. Those systems could be changed into analytic systems by two transformations with the help of computer algebra system MATHEMATICA. The conditions of uniform isochronous center are obtained. Furthermore, we prove that five limit cycles could be bifurcated from the origin. MSC:34C05, 34C07.