The Isochronous Center on Center Manifolds for Three Dimensional Differential Systems
In this paper,we present a method to study isochronous centers in 3-dimensional polynomial differential systems.Firstly,the isochronous constants of the three dimensional system are defined and recursive formulas to obtain them are given.The conditions for the isochronicity of a center are determined by the computation of isochronous constants for which there is no need to compute center manifolds of the three dimensional systems.Then the isochronous center conditions of two specific systems are discussed as an application of our method.Our method is a generalization of the formal series method proposed by Yirong Liu for determining the order of a fine focus of planar differential systems.This method with the recursive formulas can be easily implemented on a computer using a computer algebra system.
three dimensional systemisochronous centercenter manifoldisochronous constant
万方数据
维普
