逐点伪轨跟踪性质及其应用

本文给出紧致度量空间逐点伪轨跟踪性质的定义,该定义是伪轨跟踪性质定义的推广.作为应用,证明如下结论:(i)若f具有逐点伪轨跟踪性质,且对任意k∈Z ,fk为链转换的,那么对任意k∈Z ,fk为开集转换;(ii)若f具有逐点伪轨跟踪性质,且对任意n∈Z ,fn为链转换的,则f具有初始敏感依赖性质;(iii)若f为开集混合的,且具有逐点伪轨跟踪性质,那么f具有性质P;(iv)设f:(X,d)→(X,d)是同胚映射,那么f具有逐点伪轨跟踪性质当且仅当移位映射σf具有逐点伪轨跟踪性质.     

伪轨跟踪与完全正熵

本文主要给出了紧致度量空间上的连续满射f具有完全正熵的一个必要条件及当f具有伪轨跟踪性质时,f有完全正熵的一些等价条件．     

伪轨跟踪与一致正熵

本文对于满足伪轨跟踪性质的紧致度量空间上的连续满射f，给出了f具有一致正熵的几个充要条件和一个必要条件．     

时变参数动力系统的两种跟踪性质

在时变参数动力系统中引入链传递,伪轨跟踪以及渐进伪轨跟踪的概念,并通过这些概念讨论时变参数动力系统的伪轨跟踪和渐进伪轨跟踪的性质.证明了扩张的时变参数动力系统满足伪轨跟踪性质蕴含其满足渐近伪轨跟踪性质;论证了时变参数动力系统的积系统满足伪轨跟踪和渐进伪轨跟踪性质的充要条件是其每一个分系统也满足相应的性质.最后构造出了一个时变参数动力系统的例子:(∑∞X,F),证明了(∑∞X,F)是拓扑传递的,并且满足渐近伪轨跟踪性质.     

提升和投射具有伪轨跟踪性质或可扩性的连续流

本文证明了紧度量空间上的连续流经提升或投射后，其伪轨跟踪性质及可扩性是不变的；做为应用给出了不定向闭曲面上具有伪轨跟踪性质的Ｃｒ流的特征。     

数学研究与评论第25卷(2005)第1,2,3期目次

第一期 入凡的最大凡,3填充设计和最小价,3覆盖设计(英)........................……康庆德,王志芹(l) 材人(C)中的不可约性(英)......................................……,.……何华,蒋春澜,赵亮(17) 逐点伪轨跟踪性质及其应用(英)..................................……,     

tvs锥度量空间上同胚映射的可扩性

设$f$是紧tvs锥度量空间上同胚映射. 本文证明了$f$是tvs锥可扩的当且仅当$f$有生成元. 进一步, 如果$f$是tvs锥可扩的,则具有收敛半轨的点集是可数集. 本文的这些结果改进了拓扑动力系统的一些可扩同胚定理, 将有助于研究tvs锥度量空间上同胚映射的动力性质.     

定向闭曲面上具有伪轨跟踪性质的C~r流

本文给出了定向闭曲面上具有伪轨跟踪性质的 C~r(r≥2)流的特征.     

迭代函数系统的伪轨特殊性和平均跟踪性质

研究了迭代函数系统IFS(F)的伪轨特殊性与平均跟踪性质.结合经典动力系统的相关方法,证明了:如果IFS(F)有伪轨特殊性质,则它有平均跟踪性质;如果IFS(F)有平均跟踪性质并且F中某些f有稠密的0-回复点,则IFS(F)是拓扑传递的.     

伪轨跟踪性质与不变概率测度

本文利用遍历理论讨论有伪轨跟踪性质的紧致度量空间上的连续满射所具有的动力性质和混沌性态．     

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。     

Recurrence and the asymptotic pseudo-orbit tracing property

In this paper, asymptotic pseudo-orbits and the asymptotic pseudo-orbit tracing property are considered for continuous maps from a compact metric space into itself. We investigate transitive properties and recurrent properties for a map with the asymptotic pseudo-orbit tracing property. In particular, a condition for which a homeomorphism is a non-wandering homeomorphism is obtained.     

Topological Stability and Pseudo-orbit Tracing Property for Homeomorphisms on Uniform Spaces

In this paper, we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces. We introduce the concept of topological stability for homeomorphisms on compact uniform spaces and prove that if a homeomorphism on a compact uniform space is expansive and has pseudo-orbit tracing property, then it is topologically stable. Moreover, we discuss the topological stability for homeomorphisms on uniform spaces from the view of localization.We introduce defi...     

Implications of pseudo-orbit tracing property for continuous maps on compacta

We look at the dynamics of continuous self-maps of compact metric spaces possessing the pseudo-orbit tracing property (i.e., the shadowing property). Among other things we prove the following: (i) the set of minimal points is dense in the non-wandering set Ω(f), (ii) if f has either a non-minimal recurrent point or a sensitive minimal subsystem, then f has positive topological entropy, (iii) if X is infinite and f is transitive, then f is either an odometer or a syndetically sensitive non-minimal map with positive topological entropy, (iv) if f has zero topological entropy, then Ω(f) is totally disconnected and f restricted to Ω(f) is an equicontinuous homeomorphism.     

逆极限的不变测度和一致正熵性质

In this paper, the interconnection of some ergodic properties between a continuous selfmap and its inverse limit is studied. It has been proved that (1) their invariant Borel probability measures are identical up to homeomorphism and (2) they preserve uniform positive entropy property simuitaneously. As applications, it is also proved that the upper semi-continu-ous properties of their entropy maps are restricted each other, and the entropy map of the asymptotically h-expansive continuous map is upper semi-contlnuous, at the same time a continuous map having u, p.e. is topological weakmixing.     

幂零流形上自映射的点态原像熵的可加性

类似于拓扑熵,点态原像熵作为动力系统的不变量,也度量了紧度量空间上系统的复杂性.但至今不知其性质与拓扑熵是否完全一致,例如映射笛卡尔积的点态原像熵的可加性等.本文将把环面自映射笛卡尔积的点态原像熵的可加性,推广到紧幂零流形自映射的情形.     

On homeomorphisms with the two-sided limit shadowing property

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type.     

On partial shadowing of complete pseudo-orbits

In recent years many new definitions of shadowing, using a notion of ergodic (or average) pseudo-orbit were introduced. While, under the assumption of chain mixing, average pseudo-orbit usually can be equivalently replaced by pseudo-orbit in these definitions of shadowing, it is not completely clear when these shadowing properties (i.e. approximation of a pseudo-orbit by a real orbit on a sufficiently large set of indices) can or cannot occur. In this paper we analyze necessary and sufficient conditions for shadowing over a set with positive density (or syndetic). While we do not provide full characterization, a few relations to standard notions from topological dynamics are obtained.