Existence of invariant curves with prescribed frequency for degenerate area preserving mappings

作     者：Dongfeng ZHANG Hao WU Dongfeng ZHANG;Hao WU

作者机构：School of MathematicsSoutheast UniversityNanjing210096China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2022年第17卷第6期

页      面：1133-1155页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11001048,11571072,11771077,11871041) the Natural Science Foundation of Jiangsu Province,China(No.BK20201262) 

主　　题：Invariant curve area preserving mapping non-twist condition KAM iteration 

摘      要：We consider small perturbations of analytic non-twist area preserving mappings,and prove the existence of invariant curves with prescribed frequency by KAM *** speaking,the frequency of invariant curve may undergo some drift,if the twist condition is not *** in this paper,we deal with a degenerate situation where the unperturbed rotation angle function r→w+r^(2n+1)is odd order degenerate at r=0,and prove the existence of invariant curve without any drift in its ***,we give a more general theorem on the existence of invariant curves with prescribed frequency for non-twist area preserving mappings and discuss the case of degeneracy with various orders.