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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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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.