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

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

作　　者：HAN Yuecai LI Yong 

机构地区：[1]College of Mathematics,Jilin University,Changchun 130012,China College of Mathematics,Jilin University,Changchun 130012,China

出　　处：《Science China Mathematics》2005年第12期1656-1669,共14页中国科学：数学（英文版）

基　　金：supported by the National Outstanding Young’s Award of China;National 973 Project of China:Nonlinearity;Specialized Research Fund for the Doctoral Program of Higher Education and the Young Teacher's Foundation of Jilin University;supported by 985 Project of Jilin University.

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.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.

关 键 词：Arnold's theorem the Russmann non-degenerate condition. 

分 类 号：N[自然科学总论]