Dynamics of polynomial generalized Liénard system near the origin and infinity

2025/04/25 by Jun Zhang, Zhang, Jun
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2504.18438

Abstract

We classify all topological phase portraits of the polynomial generalized Liénard 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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