非自治格点量子Zakharov方程组的核截面的存在性及其性质

发布时间：2018-05-20 16:38

本文选题：格点动力系统 + 核截面　；参考：《温州大学》2015年硕士论文

【摘要】：动力系统是非线性科学的一个重要组成部分,它研究系统随时间演化的整体定性行为.本硕士论文主要研究非自治格点量子Zakharov方程组的若干动力学行为.论文具体安排如下：第一章是引言部分.首先,简要介绍无穷维动力系统和格点动力系统的起源,然后给出本文的选题背景以及主要工作.第二章研究非自治格点量子Zakharov方程组.首先,证明该方程组的解算子生成的过程紧致核截面的存在性；其次,给出该紧致核截面Kolmogorov-ε熵的上界估计；再次,证明该核截面的上半连续性；最后,给出了该紧致核截面的分形维数估计.第三章是论文小结.
[Abstract]:Dynamical system is an important part of nonlinear science. It studies the global qualitative behavior of the system over time. In this thesis, some dynamical behaviors of nonautonomous lattice point quantum Zakharov equations are studied. The specific arrangement of the thesis is as follows: the first chapter is the introduction. Firstly, the origin of infinite dimensional dynamical system and lattice dynamic system is briefly introduced, and then the background and main work of this paper are given. In chapter 2, the nonautonomous lattice quantum Zakharov equations are studied. First, we prove the existence of compact kernel cross section in the process of generating the solution operator of the equations; secondly, we give the upper bound estimate of Kolmogorov- 蔚 entropy of the compact kernel section; thirdly, we prove the upper half continuity of the kernel section; finally, The fractal dimension of the compact kernel section is estimated. The third chapter is the summary of the thesis.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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