ON EQUILIBRIA AND PERIODIC ORBITS OF COOPERATIVE SYSTEMS IN R~3

In the paper we present new criteria for existence of equilibria and periodic orbits for 3-dimensional systems which are cooperative. Particular attention is given to the relations of equilibria, cycle K and stable manifold of K. Meanwhile, the results of Hirsch [1, Theorem 9] and Jiang [2] are improved.     

向量场的旋度判定平面(空间)微分系统闭轨的不存在性

利用向量场的旋度 ,我们可判定平面、空间微分系统闭轨的不存在性 ,得到类似 Bendixson,Dulac判断法的一种新判定法 .同时还得到平面微分系统闭轨存在时的相对位置     

关于亏零p-块的一些结果

本文研究了亏零p-块的存在性,得到一些亏零p-块存在的群论条件。     

Existence of infinitely many homoclinic orbits to Aubry sets for positive definite Lagrangian systems

In this paper, we study the problem of homoclinic orbits to Aubry sets for time-periodic positive definite Lagrangian systems. We show that there are infinitely many homoclinic orbits to some Aubry set under the conditions that the associated Mather set is uniquely ergodic and the first relative homology group of the projection of this Aubry set is nonzero.     

Theory of electronic light scattering in lateral superlattices with Rashba spin–orbit coupling under quantizing electric and magnetic fields

The influence of an in-plane electric and out-of-plane magnetic field on the electronic light scattering is calculated for a lateral semiconductor superlattice within Rashba spin–orbit interaction. Sharp resonances are predicted to appear when the Raman shift matches one frequency of the Wannier–Stark ladder. The spin–orbit interaction gives rise to a dispersion of the exact one-particle eigenstates and an associated finite width of the Raman line, which can be tuned by the electric and magnetic field. When the Bloch frequency is located in this Raman line, a Fano resonance is observed.     

Mesoscopic spin-dependent reflection experiments on InSb- and InAs-based heterostructures

Spin–orbit interaction in two-dimensional electron systems can lead to a spin-dependent reflection of carriers off a lithographic barrier. Scattering of a spin-unpolarized beam from the barrier leads to the creation of two fully spin-polarized side beams in addition to an unpolarized specularly reflected beam. We experimentally demonstrate a method to create spin-polarized beams of ballistic electrons in mesoscopic samples fabricated on InSb/InAlSb and InAs/AlGaSb heterostructures. We describe two geometries, one open and one closed, in which the spin-dependent reflection and spin-dependent semiclassical trajectories were observed.     

江苏-西部能源需求-供给模型及其动力学分析

根据江苏省能源需求与西部能源供给及江苏省能源进口量之间相互支持、相互制约的复杂关系建立了江苏-西部能源需求-供给系统．分析了系统的稳态、周期、分叉、混沌等若干动力学行为．通过调节参数可以使系统处于稳定发展或周期震荡区域中．基于Silnikov定理,应用待定系数法,求出了能源系统的同宿轨的表达式．证明了在两个平衡点处均有Silnikov型的同宿轨．根据Silnikov定理确保了能源系统有Smale马蹄和马蹄形混沌．     

表面等离极化激元对电荷输运影响的自洽场理论研究Ⅱ——MIM体系分子轨道场的计算与分析

采用自洽场方法计算MIM体系在电场作用下分子场系数、态密度和局域电子态密度的变化.结果表明，分子场系数分布呈现弦函数形式；随电场增大，能带向深能量延伸并且能级峰间分离的更明显，以及构成电流通道的3d_m群原子轨道交叠态的重叠量增大，提高 了电荷输运的能力.该分析为探讨SPP对电荷输运影响的建立奠定了基础. 关键词： 分子轨道场系数 电流通道 态密度 局域电子态密度     

区间上单峰扩张自映射周期轨道的超旋转对

设f是区间I=[0,1]上的单峰扩张自映射, k ∈N,m≥2,λm,k是方程x(k-1)m(xm- 1)Q(x,m 1) (x(k-1)m-1)Q(x,m)=0在(1, ∞)上的唯一实根,其中Q(x,m)=(xm- 2xm-1 1).本文证明:若f的扩张常数λ≥λm,k,则f有超旋转对为(k,km 1)的周期轨道. 此外,还指出,当1<λ<λm,k时,在区间上存在单峰扩张自映射具有扩张常数λ却无超旋转对为(k,km 1)的周期轨道.     

Bifurcations of heteroclinic loops

By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system is established in a neighborhood of the heteroclinic loop Γ to study the bifurcation problems of homoclinic and periodic orbits. Asymptotic expressions of the bifurcation surfaces and their relative positions are given. The results obtained in literature concerned with the 1-hom bifurcation surfaces are improved and extended to the nontransversal case. Existence regions of the 1-per orbits bifurcated from Γ are described, and the uniqueness and incoexistence of the 1-hom and 1-per orbit and the inexistence of the 2-hom and 2-per orbit are also obtained. Project supported by the National Natural Science Foundation of China (Grant No. 19771037) and the National Science Foundation of America # 9357622. This paper was completed when the first author was visiting Northwestern University.