一类含有参数和有理奇性哈密顿系统的同宿与异宿轨道

Homoclinic and heteroclinic orbits in a class of Hamiltonian systems with parameters and rational singularity

研究一类含有两个参数和有理奇性平面哈密顿系统的同宿与异宿轨道.该问题来源于一个关于聚合物流体剪切流动特性的研究.借助常微定性理论和不变流形分析的方法,文中给出了系统存在同宿与异宿轨道的条件,并通过数值计算检验了所得理论结果.

The paper is devoted to the studying of the homoclinic and heteroclinic orbits in a class of planar Hamiltonian systems with parameters and rational singularity.This problem is originated from an investigation on the behaviour of polymeric fluid in shear flow.By means of qualitative theory and the analysis method of invariant manifold,precise conditions are found for the existence of heteroclinic and homoclinic orbits of the systems.In addition,some computational results are shown to verify these theoretical conclusions.