Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator  

作　　者：Li-na GUO Ai-yong CHEN Shuai-feng ZHAO 

机构地区：[1]School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023,China [2]Department of Mathematics,Hunan First Normal University,Changsha 410205,China [3]School of Mechatronics Engineering,Henan University of Science and Technology,Luoyang 471023,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第3期577-599,共23页应用数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(No.12301197);Natural Science Foundation of Henan(No.232300420343);Science and Technology Research Project of Henan Province(No.232102210057);Scientific Research Foundation for Doctoral Scholars of Haust(No.13480077);Natural Science Foundation of Hunan(No.2021JJ30166)。

摘　　要：This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator.Such systems have the form x=-y+xf(x,y),y=x+yf(x,y),where f(x,y)=a_(1)x+a_(2)xy+a_(3)xy^(2)+a_(4)xy^(3)+a_(5)xy^(4)=xσ(y),and any zero of 1+a_(1)y+a_(2)y^(2)+a_(3)y^(3)+a_(4)y^(4)+a_(5)y^(5),y=y is an invariant straight line.At last,all global phase portraits are drawn on the Poincare disk.

关 键 词：global phase portraits uniform isochronous center polynomial commutator invariant straight lines 

分 类 号：O175[理学—数学]