一类平面可积二次非Hamilton系统的Poincare'分支  

Poincare Bifurcation of the Plane Non-Hamilton Integral System

作　　者：王冲[1] 

机构地区：[1]大庆师范学院数学科学学院,黑龙江大庆166400

出　　处：《生物数学学报》2013年第4期656-664,共9页Journal of Biomathematics

基　　金：黑龙江省自然科学研究基金;大庆师范学院青年基金(09ZQ03)

摘　　要：文章研究了一类可逆情况下,可积非Hamilton系统在二次多项式扰动下的Poincare分支问题,此类问题归于弱化的Hilbert第16问题,等价于研究Abel积分的零点个数.首先采用适当的坐标变换,借助于数学软件Matlab的符号计算功能,将Abel积分写成三个线性无关的函数形式;再利用Picard-Fuchs方程和Riccati方程法,得出此系统的Poincare分支可以扰动出极限环的个数为2≤n≤3.This thesis mainly focuses perturbations in reversible case. A class of on the non-Hamilton integral system with quadratic Poincare bifurcation systems for quadratic systems with a bound of parabola and a single center is solved.This problem belongs to the weak Hilbert 16th problem which equals to determing the number of zeros of Abel integral Firstly adopting the appropriate coordinate transformation to Abel integral, by using the symbolic computation function of mathematical software matlab.We get Abel integral with linearly independent func- tion; Secondly, Picard-Fuchs equation and Riccati equation method is used. So this system with perturbation exists limit cycles between two and three.

关 键 词：可积非HAMILTON系统 POINCARE分支 ABEL积分 零点个数 极限环 

分 类 号：O175[理学—数学]