一类三维系统的次调和解与不变环面的分支  

Bifurcation of Subharmonic Solutions and Invariant Tori of a Three-dimensional System

作　　者：刘宣亮[1] 刘永奇[2] 

机构地区：[1]华南理工大学理学院数学系,广东广州510640 [2]华南理工大学自动化科学与工程学院,广东广州510640

出　　处：《数学的实践与认识》2010年第21期193-202,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10871074)

摘　　要：讨论一类三维自治系统的闭轨在周期扰动下的分支问题.利用Poincare映射与积分流形定理,得到扰动系统存在次调和解和不变环面的条件,以及次调和解的鞍结点分支.We study bifurcations of a closed orbit of a three-dimensional system under periodic perturbation.By using Poincare map and integral manifold theory,sufficient conditions for the existence of subharmonic solutions and invariant tori of the perturbed system are obtained.Moreover,saddle-node bifurcations of subharmonic solutions are studied.

关 键 词：分支 次调和解 不变环面 

分 类 号：O174.3[理学—数学]