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arXiv · 2505.21871

Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems

Jaume Llibre·Yilei Tang·Jiang Yu·Pengyu Zhou
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Abstract

In this paper we obtain the global dynamics and phase portraits of quadratic and cubic quasi-homogeneous but non-homogeneous systems. We first prove that all planar quadratic and cubic quasi-homogeneous but non-homogeneous polynomial systems can be reduced to three homogeneous ones. Then for the homogeneous systems, we employ blow-up method, normal sector method, Poincar\'e compactification and other techniques to discuss their dynamics. Finally we characterize the global phase portraits of quadratic and cubic quasi-homogeneous but non-homogeneous polynomial systems.

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Jaume Llibre, Yilei Tang, Jiang Yu, Pengyu Zhou. 2025-05-28. Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems. https://arxiv.org/abs/2505.21871

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