On the local center of an analytic Liénard system

• Autores: M. Hayashi
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 63, Nº. 1-2, 2002, págs. 93-102
• Idioma: inglés
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• Resumen

  • 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.