Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions  

作　　者：Kun WANG Junxiang XU 

机构地区：[1]School of Mathematics,Southeast University,Nanjing 211189,China

出　　处：《Frontiers of Mathematics in China》2020年第3期571-591,共21页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11871146,11671077);the Innovation Project for college postgraduates in Jiangsu Province(No.KYZZ160113).

摘　　要：We consider a class of analytic area-preserving mappings Cm-smoothly depending on a parameter.Without imposing on any non-degeneracy assumption,we prove a formal KAM theorem for the mappings,which implies many previous KAM-type results under some non-degeneracy conditions.Moreover,by this formal KAM theorem,we can also obtain some new interesting results under some weaker non-degeneracy conditions.Thus,the formal KAM theorem can be regarded as a general KAM theorem for areapreserving mappings.

关 键 词：Area-preserving mapping invariant curve KAM iteration nondegeneracy condition 

分 类 号：O18[理学—数学]