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On the local center of an analytic Liénard system

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Summary.

A necessary and sufficient condition for an analytic Liénard system \( \dot{x} = y \), \( \dot{y}=-f(x)y-g(x) \) 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.

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Technology, Nihon University, 7—24—1 Narashinonai, Funabashi-shi, Chiba 274-8501, Japan, e-mail: mhayashi@penta.ge.cst.nihon-u.ac.jp, Japan

    M. Hayashi

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  1. M. Hayashi
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Received: March 1, 1999, revised version: October 12, 2000.

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Hayashi, M. On the local center of an analytic Liénard system. Aequat. Math. 63, 93–102 (2002). https://doi.org/10.1007/s00010-002-8008-6

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  • DOI: https://doi.org/10.1007/s00010-002-8008-6

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