The Global Topological Classification And Coefficient Conditions Of The Planar Homogenous Sixth Polynomial Differential System

In this paper, we study the global topological classification and coefficient conditions of the planar homogenous sixth polynomial differential systemWhereα₆₀≠0 and it satisfies with undetermined sign case.The main techniques used in this paper included higher-degree singular pointe and polynomial theories.This paper was extended of predecessors by raising degree of planar homogenous polynomial differential system.The obvious differents that its global topological classification included what of second and fouth,while there were new topological structures. In discussing process we have gaven 344 global structures,that is, 45 topological structures.The exact synopsis as follows:In first chapter mainly gave some concepts and lemmas, meanwhile, introduced the development history of differential equation and status quo of planar homogenous system.In second chapter exactly studied all special directions of the planar homogenous sixth polynomial differential system and gave the coefficient conditions of special direction and 344 global structures of it.Because of the locality topological structure complexity of singular point O(0,0),we specially gave all the types of it,and advanced some hypothesises inlast chapter.