On Decompositions of Compact Convex Sets

The present paper generalizes M. Edelstein's theorem on the indecomposability of compact convex sets in locally convex linear topological spaces to spherical and hyperbolic geometry. Moreover, the indecomposability of compact intervals in EU¹ w.r.t. homeomorphisms of EU¹ onto itself is shown.     

The nonexistence of sensitive commutative group actions on graphs

In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

GLOBAL LINEARIZATION OF DIFFERENTIAL EQUATIONS WITH SPECIAL STRUCTURES

This paper introduces the global linearization of the differential equations with special structures.The function in the differential equation is unbounded.We prove that the differential equation with unbounded function can be topologically linearlized if it has a special structure.     

On some properties of orientation-preserving surjections on the circle

Some properties of orientation-preserving surjections with nonempty set of periodic points are studied. In particular, orientation-preserving homeomorphisms of the whole circle S ¹ are considered.      

Isomorphisms Between Groups of Homeomorphisms

We give simple conditions which ensure that the topological structure of a manifold is completely determined by a group of homeomorphisms. The reasonings are still valid in the smooth category.     

A representation of one-dimensional attractors ofA-diffeomorphisms by hyperbolic homeomorphisms

We give a representation for the restrictions ofA-diffeomorphisms of closed orientable surfaces of genus > 1 from a homotopy class containing a pseudo-Anosov diffeomorphism to all one-dimensional attractors that do not contain special pairs of boundary periodic points. The representation is given by the restriction of a hyperbolic homeomorphism to an invariant zero-dimensional set formed by the intersection of two transversal geodesic laminations. It is shown how this result can be generalized to the representation of the restrictions ofA-diffeomorphisms defined on a closed surface of any genus to arbitrary one-dimensional attractors. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 76–87, July, 1997. Translated by V. E. Nazaikinskii     

关于具有可积伸张同胚的紧性

具有可积球伸张的同胚的偏差定理、等度连续性和紧性被得到．