同宿

So before applying Mather's theorem of connecting orbits to concrete Hamiltonian system, we have to check whether the set W〓 is empty or not, and which cohomology classes are C-equivalent. In present paper, by investigating the topological structure of action minimizing sets near a co-dimensional one torus which is preserved under generic perturbations and becomes hyperbolic in nearly integrable Hamiltonian system.

与传统的Poincaré-Melnikov方法相比，我们方法明显优越之处在于，一方面我们的方法不仅可以得到双曲环面之间的异宿轨道，而且当该环面附近的其它环面破裂时，可以得到不同Mather集之间的连接轨道，另一方面，我们把异宿轨的存在性的证明转化为双曲环面极小同宿轨的某种弱孤立性的证明，所需条件比Poincaré-Melnikov方法弱得多。

We study cuspidal loop bifurcation、 Homoclinic or double Homoclinic bifurcation、 Hopf bifurcation and obtain the necessary conditions to generate limit cycles by using the coefficients of the expansion of the first Melnikov function.

利用一阶Melnikov函数的展开式的系数研究了尖点环分支、同宿分支、双同宿分支和Hopf分支，并给出了产生极限环的充分条件。

An existence theorem concerning denumerable 1-homoclinic orbits and countable families of 1-periodic orbits was given under a generic condition; and an intuitionistic de script ion about those orbits was also given.

证明在通有条件下，该异宿环附近存在可数无穷多条1-同宿轨，和可数无穷多个1-周期轨的单参数族，同时对这些周期轨和同宿轨作了直观描述。

In Chapter 3, a certain polynomial Hamilton system with 3 degree is given. By elliptic integral formulas, the monotonicity of the periodic orbits of this system is verified.

在众多文章中，讨论次谐轨的分岔都需要一个条件，那就是在同宿轨附近的周期轨是单调的，第三章给出了一个具体的三次平面Hamilton系统，利用椭圆积分公式验证了这个系统的一对同宿轨附近的周期轨的周期是单调的，这包含了三种情况，周期轨在右边同宿轨内部，在左边同宿轨内部以及在整个同宿轨圈外部。

For the homoclinics taking on values in the unbounded domain, in order to apply the usual "Mountain Pass " theorem, A compact embedding theorem is proved.

为克服同宿解取值于无界域而缺乏自然紧性，证明了一个紧嵌入定理，从而可以利用通常的山路引理与对称山路引理获得同宿解的存在性与多重性条件。

In the paper we consider a wide class of slow-fa.st second order systems and give sufficient conditions for the existence of a singular limit cycle related to a homoclinic orbit.

本文研究一类正二阶快-慢系统中奇性同宿轨道和极限环，并且给出了此系统存在奇性同宿轨道和极限环的充分条件。

Melnikov method is employed to study the bifurcations and chaos of homoclinic and subharmonic orbits for two pendulum systems.

用Melnikov方法研究具有弱阻尼与参数激励的单摆以及倒摆运动的同宿轨道分岔、次谐分岔和混沌现象，得到了发生同宿轨道分岔、次谐分岔和混沌的临界参数，并将所得理论结果与倒摆运动的实验结果进行了比较与讨论。

At first, we give the more precisely expression of the system in some sufficiently small neighborhood of the saddle point under some suitable transformation, and use the foundational solutions of the linear variational equation of the unperturbed system along the homoclinic or heteroclinic orbits as the demanded local coordinate system.

首先，我们在鞍点的充分小邻域内给出系统在适当的变换下的更加精确的表达形式，利用未扰系统沿同宿，异宿环的线性变分方程的基本解组作为系统在同宿，异宿环的小管状邻域内的新的局部坐标系。

In Chapter Ⅲ, the global stability and global attractivity of some planar autonomous systems are dealed with.

第二章考虑平面自治系统同宿轨族的一些定性性态，证明了系统至多存在一个最大椭圆扇形，得到此系统的轨线趋于奇点及同宿轨族、闭轨族、双曲扇形和椭圆扇形的存在性与不存在性的充分或充要条件。

The presence of homoclinic tangencies and homoclinic intersection makes it very difficult, sometimes even impossible, to estimate the shadowing trajectory of the non-hyperbolic nonlinear system.

摘要同宿切面和同宿截面的存在使得非双曲线型非线性系统重影轨迹的估计变得十分困难。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。