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

A class of planar non-analytic systems whose angular speed is constant is investigated in this paper. Those systems could be changed into analytic systems by two transformations, and the recursive formulas to compute the Lyapunov constants are given. Futhermore, with the help of computer algebra system MATHEMATICA, a class of quasi-cubic systems and a class of quasi-quintic systems are investigated, conditions of uniform isochronous center are obtained.