随机哈密尔顿系统的周期变差解和近不变环面解  

Periodic Variation Solutions and Tori like Solutions for Stochastic Hamiltonian Systems

作　　者：朱俊 黎泽 ZHU Jun;LI Ze(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《应用数学》2021年第2期477-488,共12页Mathematica Applicata

基　　金：Supported by the Start-up Funds for Scientific Research of High-Level Talents in Ningbo University(029-422003302)。

摘　　要：本文研究具有随机扰动的哈密顿系统的重现现象,尤其是轨道随机周期变差解和近不变环面解.具体来说,对线性薛定谔方程,我们完整阐述了随机周期变差解何时存在;对随机扰动的近可积哈密顿系统,我们证明了近不变环面的存在性与驱动噪声对应的哈密顿函数的对合性相关.In this paper, we study recurrence phenomenon for Hamiltonian systems perturbed by noises, especially path-wise random periodic variation solution(RPVS)and invariant tori like solution. Concretely speaking, for linear Schrodinger equations,we completely clarify when RPVS exists, and for nearly integrable Hamiltonian systems perturbed by noises we prove that the existence of invariant tori like solutions is related to the involution property of multi component driven Hamiltonian functions.

关 键 词：随机动力系统 哈密尔顿系统 重现现象 不变环面 

分 类 号：O211.63[理学—概率论与数理统计]