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arXiv · 2504.18438

Dynamics of polynomial generalized Li\'enard system near the origin and infinity

Jun Zhang
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Abstract

We classify all topological phase portraits of the polynomial generalized Li\'enard system, determined by three arbitrary polynomials, at the origin and the infinity. This yields a complete characterization of monodromy at the origin and the infinity. Moreover, we obtain a necessary and sufficient condition for the local center via Cherkas' method. When the origin is the only equilibrium and it is a center, there are 5 global phase portraits, including two types of global center. Further, we prove that the global center is not isochronous.

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Jun Zhang. 2025-04-25. Dynamics of polynomial generalized Li\'enard system near the origin and infinity. https://arxiv.org/abs/2504.18438

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