两类一致等时系统的中心条件和极限环分支

Center Conditions and Limit Cycle Bifurcations for Two Classes of Rigid Systems

对于一类六次一致等时系统,给出原点为中心的充要条件,并证明从细焦点至多可分支出3个极限环;对于一类七次一致等时系统,给出原点为中心的充要条件,并证明从细焦点至多可分支出4个极限环。

For a class of six order rigid systems,the necessary and sufficient conditions for the origin to be center are given.And the maximal number of limit cycles bifurcating from the weak focus is proved to be 3 .For a class of seven order rigid systems,the necessary and sufficient conditions for the origin to be center are given.And the maximal number of limit cycles bifurcating from the weak focus is proved to be 4.