迭代的计算与估计

对高次多项式函数这类非线性映射给出了一般 n次迭代的一个计算结果 ,还讨论了一维欧氏空间中一些非多项式型映射的迭代 .在二维欧氏空间中 ,我们给出了几类特殊的非线性迭代的结果 .对于一些难以精确计算迭代表达式的映射 ,我们给出了其迭代的估计 .     

Brauer第24问题的推广

本文对Ｂｒａｕｅｒ第２４问题［１］作了推广．利用Ｄａｄｅ关于循环块的理论得到如下结果：设Ｇ是有限群，Ｐ是Ｇ的循环Ｓｙｌｏｗｐ子群．设｜Ｐ｜＝ｐａ，ａ为正整数．令Ｐｉ为Ｐ中唯一的ｐｉ阶子群，１ｉａ．则｜Ｃｌ（Ｇ）｜＝｜Ｃｌ（ＮＧ（Ｐｉ））｜的充分必要条件为ＰｉＧ．     

Topologically conjugate Kleinian groups

Two Kleinian groups and are said to be topologically conjugate when there is a homeomorphism such that . It is conjectured that if two Kleinian groups and are topologically conjugate, one is a quasi-conformal deformation of the other. In this paper generalizing Minsky's result, we shall prove that this conjecture is true when is finitely generated and freely indecomposable, and the injectivity radii of all points of and are bounded below by a positive constant.

     

基于有限非阿贝尔群的密钥交换

从一般线性群GL（n,F）和对称群Sn上的困难问题出发,构造了几个密钥交换算法,新算法具有更高的效率.同时,指出基于一般线性群的密钥交换算法的安全性直接依赖于广义矩阵覆盖问题,基于对称群的密钥交换协议的安全性直接依赖于置换群上的共轭问题.     

有限群共轭类长度的一点注记

假设G=AB是子群A和B的互相置换积。通过A?B中元素的共轭类长度给出了群G的结构,推广了一些最近的结论。     

Smooth Linearization for a Saddle on Banach Spaces

As a continuation of a previous work on linearization of class C¹ of diffeomorphisms and flows in infinite dimensions near a fixed point, in this work we deal with the case of a saddle point with some non-resonance restrictions for the linear part. Our result can be seen as an extension of results by Hartman [Boletin de la Sociedad Matematica Mexicana 5(2), 220–241 (1960)] and Aronson, Belitskii and Zhuzhoma [Introduction to the Qualitative Theory of Dynamical systems on surfaces, AMS Transl. Math. Monog. vol.153, pp. 268–277 (1996)] in dimension two. We also present an application to a system of nonlinear wave equations.AMS Subject Classifications: Primary: 35B05, 34G20. Secondary: 35B40, 34D05.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday     

On perturbations of the group of shifts on the line by unitary cocycles

It is shown that the class of perturbations of the semigroup of shifts on by unitary cocycles with the property (where is the Hilbert-Schmidt class) contains strongly continuous semigroups of isometric operators, whose unitary parts possess spectral decompositions with the measure being singular with respect to the Lebesgue measure. Thus, we describe also the subclass of strongly continuous groups of unitary operators that are perturbations of the group of shifts on by Markovian cocycles with the property .

     

REPELLERS FOR MULTIFUNCTIONS OF SEMI-BORNOLOGICAL SPACES

In this article the notion of repeller for multifunctions from the viewpoints of semi-bornologicul spaces is considered. The concept of lower semi-continuous multifunctions is extended by the use of semi-bornological spaces. Semi-bornological vector spaces are studied. The notion of conjugacy for semi-bornological multifunctions is considered. The persistence of repeller under conjugate relation is proved.