近可积Hamilton系统拟有效稳定性的推广

吉林大学学报(理学版) ›› 2025, Vol. 63 ›› Issue (2): 340-0346.

近可积Hamilton系统拟有效稳定性的推广

李宏田¹, 左平², 张博森³

1. 中国刑事警察学院基础部, 沈阳 110854; 2. 三亚学院新能源与智能网联汽车学院, 海南三亚 572022; 3. 吉林大学数学学院, 长春 130012

收稿日期:2024-07-12 出版日期:2025-03-26 发布日期:2025-03-26
通讯作者: 左平 E-mail:363509677@qq.com

Generalisation of Quasi-effective Stability for Nearly Integrable Hamiltonian Systems

LI Hongtian¹, ZUO Ping², ZHANG Bosen³

1. Department of Foundation, Criminal Investigation Police University of China, Shenyang 110854, China;
2. School of New Energy and Intelligent Networked Automobile, University of Sanya, Sanya 572022, Hainan Province, China;
3. College of Mathematics, Jilin University, Changchun 130012, China

Received:2024-07-12 Online:2025-03-26 Published:2025-03-26

摘要/Abstract

摘要： 考虑对近可积Hamilton系统拟有效稳定性进行推广. 在KAM(Kolmogorov-Arnold-Moser)型非退化条件下, 给出近可积广义Hamilton系统和Poisson系统的拟有效稳定性定理, 与一般的Hamilton系统不同, 所讨论的广义Hamilton系统和Poisson系统的作用变量和角变量一般可以具有不同的维度.

关键词: 拟有效稳定性, 近可积广义Hamilton系统, Poisson系统, KAM型非退化条件

Abstract: We considered extending the quasi-effective stability for nearly integrable Hamiltonian systems. We gave the quasi-effective stability theorems for nearly integrable generalized Hamiltonian systems and Poisson systems under the KAM (Kolmogorov-Arnold-Moser) type non-degenerate condition. Unlike the general Hamiltonian systems, the action variables and angular variables of the generalized Hamiltonian systems and Poisson systems under discussion could generally have different dimensions.

Key words: , quasi-effective stability, nearly integrable generalized Hamiltonian system, Poisson system, KAM type , non-degenerate condition

中图分类号:

O175.1

李宏田, 左平, 张博森. 近可积Hamilton系统拟有效稳定性的推广[J]. 吉林大学学报(理学版), 2025, 63(2): 340-0346.

LI Hongtian, ZUO Ping, ZHANG Bosen. Generalisation of Quasi-effective Stability for Nearly Integrable Hamiltonian Systems[J]. Journal of Jilin University Science Edition, 2025, 63(2): 340-0346.