Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems
Dynamical Systems
2025-05-29 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2505.21871,
title = {Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems},
author = {Jaume Llibre and Yilei Tang and Jiang Yu and Pengyu Zhou},
journal= {arXiv preprint arXiv:2505.21871},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:1708.03437