一类3D混沌系统的异宿轨道和backstepping控制

基于异宿轨道Shilnikov准则,分析了一类三维自治微分系统异宿环的存在性,并证明了该系统具有Smale马蹄意义的混沌.然后对系统的分岔,Lyapunov指数,Poincare映射进行了数值分析,同时利用自适应反步控制方法,对含有三个未知参数的系统给出了一种控制算法.最后通过数值示例进行仿真,对文中论述进行了验证. 关键词： 异宿环 自适应反步 Shilnikov准则 Poincare映射     

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.     

Quadrangulations of sphere and ball quotients

We give a classification of sphere quadrangulations satisfying a condition of non‐negative curvature, following Thurston's classification of sphere triangulations under the same condition. The generic family of quadrangulations is parametrized by the points of positive square‐norm of an integral Gaußian lattice in the six‐dimensional complex Lorentz space. There is a subgroup of automorphisms of acting on this lattice whose orbits parametrize sphere quadrangulations in a one‐to‐one manner. This group acts discretely on the corresponding five‐dimensional complex hyperbolic space; is of finite co‐volume; its ball quotient is the moduli space of unordered 8 points on the Riemann sphere, and also appears in Picard‐Terada‐Deligne‐Mostow list. Both Thurston's lattice and our lattice may be thought of as parametrizations of certain families of subgroups of the modular group; equivalently, of certain families of dessins. These families also parametrize points of a moduli space.     

One Nonparabolic End Theorem on Kahler Manifolds

In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.     

Exact constants in Poincaré type inequalities for functions with zero mean boundary traces

In this paper, we investigate Poincaré type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd.     

A SPECIAL CUBIC SYSTEM CLOSE RELATED TOTHE GENERAL QUADRATIC SYSTEM

1NumberandDistributionofCriticalPoilltsConsiderthefollowingcubicsystem:itcontainsonlytwocubictermspx'andqx'morethanthegeneralquadraticsystem:Thecoordinatesofthecriticalpointsatinfinityof(1)mustsatisfytheequation:px'y~qx'=0.(3)SoA(P,q,0)andB(0,l,0)aretheonlycriticalpointsatinfinityof(1).Itiseasilyseenthatthetwocharacteristicrootsof(1)atAareAl=AZ=--p,soAisastable(unstable)nodewhenp>0(<0).Moreover,Bisahigherordercriticalpointatinfinityof(1)withindex0,itisthepileupof3criticalpointsontheequat…     

一类摄动系统的Poincaré分叉与极限环

本文利用临界情形的隐函数存在定理讨论了一类摄动系统分支周期解的存在性与稳定性,利用后继函数法讨论了该系统极限环的存在性、唯一性和稳定性。     

再论一类二次系统的无界双中心周期环域的POincare分支

本文再一次讨论了具有双曲线与赤道弧为边界的双中心周期环域的二次系统的Poincare分支，并构造出了此系统出现极限环的(0，3)分布或出现一个三重极限环的具体例子．