一类具有双同宿轨的Hamilton系统在n次多项式扰动下的Poincare分支  

Poincare Bifurcation Problems of Hamiltonian System With Double-Homoclinic Orbit Under Polynomial Perturbation

作　　者：李维伟[1] 李宝毅[2] 魏杰[1] 马新光[2] 

机构地区：[1]军事交通学院基础部,天津300161 [2]天津师范大学数学科学学院,天津300384

出　　处：《数学进展》2011年第2期187-192,共6页Advances in Mathematics（China）

基　　金：天津市教委科技发展基金(No.20070405)

摘　　要：本文利用G.S.Petrov的复域方法研究了一类具有双同宿的Hamilton系统(x=y,y=x-x^3)在n次多项式扰动下,周期闭轨族U_(h∈(0,+∞)Γ_h={(x,y)|H(x,y)=1/2 y^2-1/2 x^2+1/4 x^4=h>0}的Poincare分支现象,及同宿闭轨分支现象,证明了扰动系统在周期闭轨族U_(h∈(0,+∞)Γ_h附近分支出极限环个数的上界为n+1.A class of the Hamilton systems（x = y,y = x -x^3） with double-homoclinic orbit under degree n polynomial perturbation is considered in this paper.We apply G.S. Petrov＇s method to study the Poincare bifurcation problems of the familys of periodic close orbit∪_（h∈（0,＋∞））Γ_h ={（x,y）｜H（x,y） = 1/2y^2- 1/2x^2 ＋ 1/4x^4 = h0} and the bifurcation problems of double-homoclinic orbit.It proves that the upper bound number of limit-cycles of the perturbed system is no more than n ＋ 1 in the neighborhood of∪_（h∈（0 ＋∞））Γ_h.

关 键 词：HAMILTON系统 Mel'nikov函数 POINCARE分支 同宿闭轨分支 

分 类 号：O175.12[理学—数学]