【摘要】 本文研究高维退化系统在小扰动下的动力学行为,在共振的情况下,利用延拓的方法,讨论了扰动 系统不变环面的保存性,并利用推广的Melnikov函数、横截性理论讨论了同宿于不变环面的横截同宿 轨道存在的条件,推广和改进了一些文献的结果.更多还原

【Abstract】 The dynamical behavior under perturbation of high dimensional degenerated system is studied. Under resonant condition, the authors use continuation method to discuss the persistence of invariant torus of perturbed system. Also the authors use extended Melnikov function, transversality theory to discuss transversality of the orbit homoclinic to invariant torus. Some known results are extended.更多还原