Arnold's theorem on properly degenerate systems with the Russmann nondegeneracy

作     者：HAN Yuecai & LI Yong College of Mathematics, Jilin University, Changchun 130012, China 

作者机构：College of Mathematics Jilin University Changchun China 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2005年第48卷第12期

页      面：1656-1669页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：985 Project of Jilin University National Outstanding Young’s Award of China Young Teacher’s Foundation of Jilin University National Key Research and Development Program of China, NKRDPC Specialized Research Fund for the Doctoral Program of Higher Education of China, SRFDP 

主　　题：Arnold’s theorem the Russmann non-degenerate condition. 

摘      要：In this paper, we investigate the persistence of invariant tori for the nearly in-tegrable Hamiltonian system H(x,y) = h(y) + εp(x,y) + ε2Q(x,y), where h(y) and εp(x,y) satisfy the Russmann non-degenerate condition. Mainly we overcome the difficulties that the order of the parameter E in the perturbation ε2Q(x,y) is not enough and that the measure estimate involves in parts of frequencies with small parameter.