拓扑遍历与拓扑双重遍历

令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在[2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质.     

拓扑遍历映射

本文研究紧致度量空间上拓扑遍历自映射的性质、判定及与混沌的关系．     

Fell拓扑,Choquet容量和遍历的 Choquet容量系统

本文描述了Fell 拓扑的结构与收敛条件,重新确立了关于随机集的Choquet 定理在概率论中的重要作用,并提出了不变Choquet 容量的概念。此外,利用环面上的双曲自同构和随机映射,具体构造了一个遍历的Choquet 容量系统,且进一步探讨了这种系统的动力性态。     

熵极小动力系统的复杂性

设X是一个紧致度量空间,f:X→X是一个连续映射,(X,f)是熵极小的.该文首先证明了f是强遍历的;另外,如果还假设X中存在f的一个真的(拟)弱几乎周期点,则得到f具有正拓扑熵且对任意的n1,f~n是遍历敏感依赖的.因此,f在Li-Yorke和Takens-Ruelle意义下是混沌的.该文所得结论改进和推广了最近的一些结论.     

WZ-Domain与WZ-Scott拓扑

引入WZ-双小于关系, 以此为基础给出WZ-Domain的概念, 讨论它的基本性质, 证明当子集系统Z满足一定条件时, WZ-Domain上的WZ-双小于关系具有插入性.其次, 在Z-完备偏序集上定义WZ-Scott拓扑, 证明在一定条件下一个映射关于该拓扑是连续映射当且仅当该映射保定向的Z集之并. 最后对WZ-Domain上的WZ-Scott拓扑的性质进行研究, 证明对一类子集系统,WZ-Scott拓扑空间是Sober空间当且仅当该拓扑空间具有Rudin性质.     

区间映射的链回归点的可链点集

主要讨论区间映射的链回归点的可链点集与链等价集的关系,证明了:若区间映射的拓扑熵是零,则它的链回归点的可链点集与链等价集相等.此外还得到了区间映射有正拓扑熵的几个等价条件.     

拟一致结构与拓扑

本文的目的是(1)指出分子格L上的拟一致结构既可在L上导出一个拓扑,又可在L上导出一个余拓扑,并研究二者的关系;(2)利用保交减值映射族来建立另一类拟一致结构理论;(3)研究两类拟一致结构之间的联系.     

序列伪轨跟踪性与拓扑可迁

给出序列伪轨跟踪性的定义,得到拓扑可迁的一个充分条件,并证明,若f是同胚,则f具有序列伪轨跟踪性当且仅当其逆极限空间上的移位映射σf具有序列伪轨跟踪性。     

广义近似空间的粗糙同胚与拓扑同胚

对广义近似空间之间的映射引入并刻画了粗糙连续性和拓扑连续性,探讨了他们的性质及相互关系.证明了两个粗糙连续映射的复合还是粗糙连续的,每个粗糙连续的映射都是拓扑连续的.在此基础上引入了粗糙同胚性质和拓扑同胚性质的概念,证明了拓扑同胚性质均为粗糙同胚性质并考察了广义近似空间的诸如分离性、连通性、紧性等的粗糙同胚不变性和拓扑同胚不变性.     

谓词转换器的拓扑语义

本文利用半拓扑空间的连续映射建立Dijkstra谓词转换器的拓扑语义。，引入D－半拓扑空间概念，用以建立相容谓词转换器的语义，引入SM-半拓扑空间概念，用以刻画连续谓词转换器的语义。针对不确定程序，本文引入了dI-domain上半稳定映射概念，给出了其等价刻画。     

CHAOS AND TOPOLOGICAL MIXING OF TREE MAPS

In the present paper we show that a tree map is totally transitive iff it is topologically mixing. Using this result, we prove that the tree maps having a chaotic (or scrambled) subset with full Lebesgue measure is dense in the space consisting of all topologically mixing (transitive, respectively) maps.     

Cantor集合上的连续自映射

本文证明了Ｃａｎｔｏｒ集Ｃ上所有拓扑共轭于（单边的）有限型子移位的连续自映射的集合在H中稠密，此外Ｃ上每个拓扑传递（混合）映射均可被拓扑共轭于有限型子移位的拓仆传递（混合）映射一致逼近．     

A Characterization of Topologically Transitive Attributes for a Class of Dynamical Systems

In this work,by virtue of the properties of weakly almost periodic points of a dynamical system (X,T) with at least two points,the authors prove that,if the measure center M(T) of T is the whole space,...     

Topologically transitive subsets of piecewise monotonic maps,which contain no periodic points

If one splits the nonwandering set of a piecewise monotonic map into maximal subsets, which are topologically transitive, one gets two kinds of subsets. The first kind of these subsets has periodic orbits dense, the second kind contains no periodic orbits. In this paper it is shown, that there are only finitely many subsets of the second kind, each of which is minimal and has only finitely many ergodic invariant Borel probability measures.     

按序列分布混沌与拓扑混合

本文讨论了按序列分布混沌与拓扑混合的关系,并证明了:若X为至少两点的可分局部紧致度量空间,连续映射f:X→X是拓扑混合的,则对于任一正整数递增序列{mi},存在X的c-稠密Fσ子集D是f按{mi}的某子序列的分布混沌集.     

The vertex-transitive TLF-planar graphs

We consider the class of the topologically locally finite (in short TLF) planar vertex-transitive graphs. We characterize these graphs by finite combinatorial objects called labeling schemes. As a result, we are able to enumerate and describe all TLF-planar vertex-transitive graphs of given degree, as well as most of their transitive groups of automorphisms. In addition,we are able to decide whether a given TLF-planar transitive graph is Cayley or not. This class contains all the one-ended planar Cayley graphs and the normal transitive tilings of the plane.     

The topology of group extensions of C systems

The paper is concerned with the topological and metric properties of group extensions of C systems. The basic theorem describes the topologically transitive component, the ergodic component, and the K component of a group extension of a C system. It is shown that each of these components is a group sub-bundle of a principal bundle in which the group extension acts. The frame flow on a manifold of negative curvature is seen to be a special case of a group of extension of a C system. It is shown that the space of frames on a compact three-dimensional manifold with negative curvature does not have any group sub-bundles, so that the frame flow on manifolds of this class is topologically transitive, ergodic, and a K system.     

Chain recurrence rates and topological entropy

We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (chain recurrence and chain mixing times). We give upper and lower bounds for these recurrence times and relate the chain mixing time to topological entropy.