Existence of Invariant Tori in Reversible Mappings

In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions,     

光滑拟周期可逆映射的不变曲线

证明了平面拟周期可逆映射在C~l光滑情况下其不变曲线的存在性,并且给出了l同不变曲线的光滑性和丢番条件中指数的关系.     

一类差分方程的不变曲线分枝

讨论一类差分方程的不变曲线分枝。由于该差分方程所定义的动力系统是可积的,故该方程的不变曲线的讨论可化为对平面Hamilton系统所定义的轨线的拓扑分类的研究。通过严格的定性分析,获得其不变曲线在参数空间内的分类。     

Invariant Curves of Reversible Mappings with Small Twist

In this paper,we are concerned with the existence of invariant curves of reversible mappings.A variant of the classical small twist theorem is given.     

一类可加和二次混合泛函方程的稳定性

本文研究了一类新的源自可加映射和二次映射的混合泛函方程f(x+2y)+f(x-2y)=f(x+y)+f(x-y)+3f(2y)-6f(y),及其在拟β赋范线性空间中的Hyers-Ulam稳定性.     

Existence of Invariant Tori for Certain Weakly Reversible Mappings

In this paper, we consider certain mappings, ${\mathcal {M}}In this paper, we consider certain mappings, ℳ , sufficiently close to an integrable one, which is weakly reversible with respct to the mappings ? sufficiently close to an involution of tye (m, n), where m, n∈Z ₊ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for providing the existence of a Cantor family of m-tori invariant under the reversible mappings ℳ and the reversing mapping ?. Received September 29, 1999, Accepted July 18, 2000     

On a Conformally Invariant Integral Equation Involving Poisson Kernel

We study a prescribing functions problem of a conformally invariant integral equation involving Poisson kernel on the unit ball. This integral equation is not the dual of any standard type of PDE. As in Nirenberg problem, there exists a Kazdan–Warner type obstruction to existence of solutions. We prove existence in the antipodal symmetry functions class.     

套子代数上线性映射的Lie不变子空间

本文引入了Banach代数上线性映射的Lie不变子空间,给出了因子VonNeumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一般形式,研究了Lie导子与Lie自同构的概念及了Lie导子与Lie自同构半群的关系.     

On a Functional Differential Equation

This paper considers some analytical and numerical aspects ofthe problem defined by an equation or systems of equations ofthe type (d/dt)y(t) = ay(t)+by(t), with a given initial conditiony(0) = 1. Series, integral representations and asymptotic expansions fory are obtained and discussed for various ranges of the parametersa, b and (> 0), and for all positive values of the argumentt. A perturbation solution is constructed for |1–| <<1, and confirmed by direct computation. For > 1 the solutionis not unique, and an analysis is included of the eigensolutionsfor which y(0) = 0. Two numerical methods are analysed and illustrated. The first,using finite differences, is applicable for < 1, and twotechniques are demonstrated for accelerating the convergenceof the finite-difference solution towards the true solution.The second, an adaptation of the Lanczos method, is applicablefor any > 0, though an error analysis is available onlyfor < 1. Numerical evidence suggests that for > 1 themethod still gives good approximations to some solution of theproblem.     

Sobolev Mappings: Lipschitz Density is not a Bi-Lipschitz Invariant of the Target

We study a question of density of Lipschitz mappings in the Sobolev class of mappings from a closed manifold into a singular space. The main result of the paper, Theorem 1.7, shows that if we change the metric in the target space to a bi-Lipschitz equivalent one, then the property of the density of Lipschitz mappings may be lost. Other main results in the paper are Theorems 1.2, 1.3, 1.6, 1.8. This work was supported by the NSF grant DMS-0500966. Received: June 2005 Revision: December 2005 Accepted: January 2006     

On a Multilinear Functional Equation

Mathematical Notes - The following functional equation is solved: $$fleft( {{x_1} + z} right) cdots fleft( {{x_2} + z} right)fleft( {{x_1} + cdots + {x_{s - 1}} - z} right) = {phi...     

An Invariant Group of MKdV Equation

In this paper, we present an invariant group of the MKdV equation q_t = q_{xxx} - 6q²q_x. By using this invariant group, we can obtain some new solutions from a known solution by quadrature.     

集值映射的函数单调性和余强制性

本文介绍几个新的集值映射的函数单调性和余强制性概念，并讨论它们与已有概念间各种可能的蕴含关系．     

Invariant Measures for a Random Evolution Equation with Small Perturbations

In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equations. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero. Received March 20,1998, Accepted June 1, 2000     

Invariant Manifolds for the Burgers Equation Defined on a Semiaxis

Stable nonlocal invariant manifolds for the Burgers equation defined on R₊ are constructed. One problem of a boundary control stabilizing the solution of this equation to zero is also studied. Results of numerical experiments are presented.     

Linearly Invariant Families of Holomorphic Mappings of a Ball. The Dimension Reduction Method

The notion of a linearly invariant family of mappings of a ball in C was introduced in the article ``Pfaltzgraff J. A., Distortion of locally biholomorphic maps of the n-ball, Complex Variables, 33, 239-253 (1997)'; it generalizes the classical case n=1 studied earlier by Ch. Pommerenke and other authors. In the indicated article, Pfaltzgraff in particular obtained and used a false equality (5.3). Application of this equality also underlies some assertions in other articles. Consequently, some theorems remain unproven. We propose the dimension reduction method which enables us to save the proof and obtain new results on linearly invariant families of mappings of a ball. The idea of the method is simple and consists in reduction of a problem posed for linearly invariant families in Cⁿ to a problem for the classical case of a disk (n=1).     

Finite-Dimensional Mappings Describing the Dynamics of a Logistic Equation with Delay

Doklady Mathematics - A family of mappings used in the numerical simulation of a delay logistic equation is considered. This equation finds wide applications in problems of mathematical ecology....