高维小扭转映射不变环面的存在性  

Existence of Invariant Tori for Small Twist Mappings with Higher Dimensions

作　　者：李宏田 所彧乔 LI Hongtian;SUO Yuqiao(Department of Foundation,Criminal Investigation Police University of China,Shenyang 110854,China;College of Science,Changchun University of Science and Technology,Changchun 130022,China)

机构地区：[1]中国刑事警察学院基础部,沈阳110854 [2]长春理工大学理学院,长春130022

出　　处：《吉林大学学报（理学版）》2022年第1期15-19,共5页Journal of Jilin University:Science Edition

基　　金：辽宁省自然科学基金指导计划项目(批准号:20180550271);中国刑事警察学院博士科研启动基金(批准号:D2015014).

摘　　要：考虑角度变量和作用变量具有不同维数的高维近可积小扭转映射不变环面的存在性,通过构造KAM迭代的方法,证明高维近可积小扭转映射在满足Rüssmann非退化条件及相交性条件下存在一族不变环面.We considered the existence of invariant tori for nearly integrable small twist mappings whose dimensional numbers of angles and actions variables were different.By constructing KAM iteration method,we proved that the nearly integrable small twist mappings with high dimension possessed a family of invariant tori under the Rüssmann non-degeneracy condition and the intersection condition.

关 键 词：KAM迭代 不变环面 小扭转映射 

分 类 号：O175.1[理学—数学]