Arnolds theorem on properly degenerate systems with the Rüssmann nondegeneracy
In this paper, we investigate the persistence of invariant tori for the nearly integrable Hamiltonian system H(x, y) =h(y) + εp((x), y) + ε2Q(x, (y)), whereh(y) and εp((x), y)the order of the parameter ε in the perturbation ε2Q(x,y) is not enough and that the measure estimate involves in parts of frequencies with small parameter.
作 者： HAN Yuecai LI Yong 作者单位： College of Mathematics,Jilin University,Changchun 130012,China 刊 名： 中国科学A辑（英文版） SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS) 年，卷(期)： 2005 48(12) 分类号： O1 关键词： Arnold's theorem the Rüssmann non-degenerate condition