On the Period Function of Liénard Systems

We study the period functionTof a centerOof a Liénard system. A sufficient condition for the monotonicity ofT, or for the isochronicity ofO, is given. Such a condition is also necessary whenfandgare analytic, andgis odd. In this case a characterization of isochronous centers of Liénard systems is given. Strict monotonicity and global monotonicity ofTare also investigated