三次平面拟齐次系统的全局结构  

Classification of Global Phase Portraits of Cubic Planar Quasi-homogeneous System

作　　者：魏怡倩 梁海华 WEI Yi-qian;LIANG Hai-hua(Guangdong Polytechnic Normal University,Guangzhou Guangdong 510665)

机构地区：[1]广东技术师范大学数学与系统科学学院,广东广州510665

出　　处：《广东技术师范大学学报》2021年第3期43-56,共14页Journal of Guangdong Polytechnic Normal University

基　　金：国家自然科学基金项目(No.11771101)资助。

摘　　要：考虑三次平面拟齐次但非齐次不可约多项式微分系统,利用拟齐次爆破法和庞加莱-李雅普诺夫紧致化分别研究有限奇点和无穷远奇点,得到了该类系统所有标准型的全局相图,并进一步证明,在拓扑等价意义下,这些相图可分为17类.This paper is devoted to the classification of global phase portraits of cubic planar quasi-homogeneous but non-homogeneous coprime polynomial differential systems.Using quasi-homogeneous blow-up technique and Poincaré-Lyapunov compactification to study finite singularities and infinite singularities,respectively,we get all global phase portraits of this type of systems with canonical forms,and then further prove that these phase portraits can be divided into 17 categories in the sense of topological equivalence.

关 键 词：拟齐次 三次 全局相图 平面系统 

分 类 号：O175[理学—数学]