Resumen de On the local center of an analytic Liénard system

M. Hayashi

• A necessary and sufficient condition for an analytic Liénard system [(x)\dot] = y, [(y)\dot]=-f(x)y-g(x) to have a local center at the origin is given. It is proved by using the Poincaré-Lyapunov method. Our results improve an old result of T. Saito. In Section 3 we illustrate our main result by numerical examples with phase portraits.