无穷维环面上向量场的可约性  

Reducibility of vector fields on infinite-dimensional tori

作　　者：黄鹏 Peng Huang

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025

出　　处：《中国科学:数学》2025年第4期803-812,共10页Scientia Sinica:Mathematica

基　　金：国家自然科学基金(批准号:12261014和11901131)资助项目。

摘　　要：本文考虑无穷维环面上向量场的可约性问题.在证明中,使用KAM(Kolmogorov-Arnold-Moser)理论的一种变形形式.在KAM迭代步骤中,引进参数q(0<q<1),使得KAM迭代步骤以函数qnε收敛而不是超指数函数收敛.新的估计技巧与迄今为止文献中关于KAM理论的内容完全不同,只保留了Kolmogorov的局部线性化思想和Moser的修正项.In this paper,we are concerned with the reducibility of vector fields on the infinite-dimensional tori.In the proof,we use a new variant of the KAM(Kolmogorov-Arnold-Moser)theory in the steps of the KAM iteration,containing an artificial parameter q(0<q<1),which makes the steps of the KAM iteration infinitely small in the speed of function qn";rather than the super exponential function.The new technique of estimation differs completely from all that has appeared about the KAM theory in the literature up to date,only Kolmogorov’s idea of local linearization and Moser’s modifying terms are left.

关 键 词：KAM理论 无穷维环面 向量场 可约性 

分 类 号：O175[理学—数学]