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| The First Integrals and Related Properties of a Class of Quintic Systems with a Uniform Isochronous Center |
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| KeyWord:First integrals; Equivalence system; Uniform isochronous center; Infinite singularity; Local phase portraits |
| Author Name | Affiliation | | Yuexin Yan | Guangling College of Yangzhou University, Yangzhou, Jiangsu 225000, China | | Zhengxin Zhou | College of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu 225002, China |
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| Abstract: |
| In this paper, we give all the first integrals of the quintic systems which have a uniform isochronous center,
and use them to determine the qualitative behavior of the periodic solutions of their equivalent non-autonomous systems. Meanwhile, we clearly describe the local phase portraits of singularity at infinity. |
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