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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 NameAffiliation
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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      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.