近可积Hamilton系统拟有效稳定性的推广  

Generalisation of Quasi-effective Stability forNearly Integrable Hamiltonian Systems

作　　者：李宏田 左平 张博森 LI Hongtian;ZUO Ping;ZHANG Bosen(Department of Foundation,Criminal Investigation Police University of China,Shenyang 110854,China;School of New Energy and Intelligent Networked Automobile,University of Sanya,Sanya 572022,Hainan Province,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[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

出　　处：《吉林大学学报(理学版)》2025年第2期340-346,共7页Journal of Jilin University:Science Edition

基　　金：辽宁省自然科学基金(批准号:20180550271);三亚学院人才引进项目(批准号:USYRC23-17)。

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.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.

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 

分 类 号：O175.1[理学—数学]