【作者】 曹阳；

【导师】 丛洪滋；

【作者基本信息】 大连理工大学 ， 应用数学， 2020， 硕士

【摘要】 本文主要讨论了格点系统里,相空间为解析空间的哈密顿系统在小扰动下的解在原点附近的长时间稳定性问题.本篇文章主要分为五个部分:第一章,我们主要介绍哈密顿系统的起源与发展和国内外研究现状,以及本篇文章的研究背景和主要结果;第二章,通过构造思想,进一步研究映射以及坐标复化的方法来证明同调方程解的存在性,并且给出解的形式;第三章,主要处理迭代过程中产生的小分母的问题.相比于有限维空间,在这里我们要对多项式划分的更细致,从而引入了对图的研究.接下来给出相应的测度估计和泊松括号范数的估计,从而得出了对余项的一个初步估计.这部分也是本篇文章的重点部分;第四章,利用上面我们得到的关系式及引理得到最终的余项估计,从而确定相应的稳定时间.第五章,总结与展望.更多还原

【Abstract】 In this paper,we mainly study the Hamiltonian system in which the phase space is analytic space,the solution of the system is about the stability of a small disturbance near the origin.This article is divided into five parts:In the first chapter,we mainly introduce the origin and development of Hamiltonian system and the research status at home and abroad,as well as the research background and main results of this paper;In the second chapter,through the idea of construction,we further study the method of mapping and coordinate complex to prove the existence of homology equation solution,and give the form of solution;In the third chapter,we mainly deal with the problem of the small denominator generated in the iterative process.Compared with the finite dimensional space,we need to divide the polynomials more carefully here,so we introduce the study of the diagrams.Next,we give the corresponding measure estimation and the estimation of the Poisson bracket norm,so we get a preliminary estimation of the remainder term.This part is also the key part of this article;In the fourth chapter,we use the above relation and lemma to get the final remainder estimation,so as to determine the corresponding stabilization time.In the fifth chapter,summary and prospect.更多还原