Global dynamics of planar quasi-homogeneous differential systems

Yilei Tang; Xiang Zhang

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arXiv · 1708.03437

Global dynamics of planar quasi-homogeneous differential systems

Yilei Tang·Xiang Zhang

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Abstract

In this paper we provide a new method to study global dynamics of planar quasi--homogeneous differential systems. We first prove that all planar quasi--homogeneous polynomial differential systems can be translated into homogeneous differential systems and show that all quintic quasi--homogeneous but non--homogeneous systems can be reduced to four homogeneous ones. Then we present some properties of homogeneous systems, which can be used to discuss the dynamics of quasi--homogeneous systems. Finally we characterize the global topological phase portraits of quintic quasi--homogeneous but non--homogeneous differential systems.

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Yilei Tang, Xiang Zhang. 2017-08-11. Global dynamics of planar quasi-homogeneous differential systems. https://arxiv.org/abs/1708.03437

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