First , we take the analysis of phase - plane on the invariant plane for the perturbed and unperturbed systems . next , we applied the singular perturbation theory to establish the persistence of invariant manifolds , as well as the " fiber represent at iones " of these manifolds . finally , by using the global integrable theory of the unperturbed system and melnikov measurement we obtai n the existence of homoclinic orbits for the cqs equation under the generalized parameters conditions 首先，我们在常值平面上对扰动和未扰动系统进行相平面分析；然后利用奇异扰动理论讨论不变流形的保持性，并给出不变流形的纤维表示；借助于未扰动系统的可积结构和melnikov测度，我们得到了三次?五次非线性schr (
In this thesis , different types of stability equations , including orr - sommerfeld equation ( ose ) and parabolized stability equation ( pse ) based on the “ slow change ” hypothesis and the local method equation which is computed in local range , are derived from navier - stokes equation with “ small disturbance ” hypothesis 本文从navier - stokes方程出发,导出不同形式的流动稳定性方程,包括采用小扰动理论得到的orr - sommerfeld方程( ose ) 、基于流向慢变特性而得到的抛物化稳定性方程( pse )以及在一小范围内计算的局部法方程。
First , we study how apply this method to the iron fiber mixture , and recognize it can be applied for this purpose only if the em parameters of the single electric fiber be obtained . second , because dyadic green function ' s singularity great effects the integral equation in sft , we resolve the calculating problem of the coefficients of singular dyadic green function 然后，由于在强扰动理论中，并矢格林函数的奇异项对求解电磁参数的积分方程起着非常关键的作用，我们解决了出现于计算等效电磁参数公式中的并矢格林函数奇异项系数的计算问题。
The forces and moments acting on the bomb are analyzed and the corresponding reference frames and motion model are built . based on disturbance theory , the mathematical model is simplified . what ' s more , taking real flight of the sgb into account , some assumptions are given . on the basis of these assumptions , the motion of the sgb is broke into the motion in vertical plane and the motion in the horizontal plane . dynamic characteristics of the motion in vertical plane is mainly studied 在此基础上，通过小扰动理论将简易制导航弹的空间运动数学模型化简，得到简易制导航弹的空间扰动运动数学模型。根据简易制导航弹的实际飞行情况，作出了一些假设条件，将简易制导航弹的空间扰动运动分解成纵向扰动运动和侧向扰动运动，并相应的得到两个通道的数学模型。
Further - more , by constructing the relations between the fiflite subshift on the symbolic set and the chaotic iterated map by means of marotto theorem , we investigate the structure of the invariant as well as the estimation of topological entropy , zeta - - function , lyapunov exponent . by the end of the chapter , we present several conclusions on the perturbed chaotic systems and a theorem about " heteroclinical repellers imply chaos " . in chapter 3 , we are mathematically modelling two particular classes of impul - sive differential equations having chaos dynamics 在本文的第三章中，我们建立了脉冲微分方程中的两类混沌模型，一类利用映射的扰动理论证明了系统随着参数变化时具有不同意义的混沌动力学行为；另一类则利用勒贝格可测的概念给出了脉冲微分方程中所特有的关于脉冲间期函数初值敏感的定义，同时理论证明了在一类脉冲微分方程中确实如新定义所描述的复杂动力学行为
We have summarized a set of theoretical approach to this problem and discussed the instability of the gas cloud and the systems composed of collisionless particles in the background of dark matter . linear perturbation theory is the method to solve this problem , in which , we add the perturbation into the equilibrium state and discussed its evolution 本文研究了自引力系统的稳定性问题，总结了解决该问题的一套理论方法。并具体研究了存在暗物质背景时气体云和无碰撞粒子系统中扰动的演化情况。解决稳定性问题的方法用线性扰动理论，即在平衡态中加入扰动，研究扰动在系统中的演化情况。
This paper is composed of three chapters . in the first chapter , the background of the optimal backward perturbation theories are introduced , and the historical development of the research on the eigenvalue problems are summarized . the main results of the optimal backward perturbation theories on eigenvalue problems are outlined 论文由三部分构成：第一章介绍了有关最佳向后扰动理论的背景，综述了关于特征值问题扰动分析研究的进展情况，简要概括了特征值问题最佳向后扰动理论的主要结果，指出研究最佳结构向后误差的意义。
