同宿流形中的奇异轨道

Singular orbits in homoclinic manifolds

研究较一般的高维退化系统的同宿、异宿轨道分支问题 .利用推广的Melnikov函数、横截性理论及奇摄动理论 ,对具有鞍 -中心型奇点的带有角变量的奇摄动系统 ,在角变量频率产生共振的情况下 ,讨论其同宿、异缩轨道的扰动下保存和横截的条件 .

The bifurcation problems of the homoclinic and heteroclinic orbits for the general degenerated system of higher dimensions are studied.By using the generalized Melnikov functions,transversal theory and singular perturbation theory,the conditions of persistence and transversality of homoclinic and heteroclinic orbits for singular perturbation system which has saddle\|center type equilibrium with a reaonance about action\|angle variables are discussed.Moreover,some known results are extended.