Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910971230945280 |
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| author | Llibre, Jaume Tang, Yilei Yu, Jiang Zhou, Pengyu |
| author_facet | Llibre, Jaume Tang, Yilei Yu, Jiang Zhou, Pengyu |
| contents | 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, Poincaré 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems Llibre, Jaume Tang, Yilei Yu, Jiang Zhou, Pengyu Dynamical Systems Classical Analysis and ODEs 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, Poincaré 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. |
| title | Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2505.21871 |