高维小扭转映射不变环面的存在性

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (1): 15-0019.

高维小扭转映射不变环面的存在性

李宏田¹, 所彧乔²

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

收稿日期:2021-08-08 出版日期:2022-01-26 发布日期:2022-01-26
通讯作者: 李宏田 E-mail:lihongtian@cipuc.edu.cn

Existence of Invariant Tori for Small Twist Mappings with Higher Dimensions

LI Hongtian¹, SUO Yuqiao²

1. Department of Foundation, Criminal Investigation Police University of China, Shenyang 110854, China;
2. College of Science, Changchun University of Science and Technology, Changchun 130022, China

Received:2021-08-08 Online:2022-01-26 Published:2022-01-26

摘要/Abstract

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.

关键词: KAM迭代, 不变环面, 小扭转映射

Abstract: 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.

Key words: KAM iteration, invariant torus, small twist mapping

中图分类号:

O175.1

李宏田, 所彧乔. 高维小扭转映射不变环面的存在性[J]. 吉林大学学报(理学版), 2022, 60(1): 15-0019.

LI Hongtian, SUO Yuqiao. Existence of Invariant Tori for Small Twist Mappings with Higher Dimensions[J]. Journal of Jilin University Science Edition, 2022, 60(1): 15-0019.