Unique Ergodicity for Zero-entropy Dynamical Systems with the Approximate Product Property

We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.     

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,...     

Modelization and Nonparametric Estimation for Dynamical Systems with Noise

We examine the effect of two specific noises (either known or small ones) on a dynamical system. We obtain consistent estimates with their rates of convergence for the invariant density in that context. We illustrate our theoretical results with simulations. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems

In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points; and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point. In the end, it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

Several Dynamics of Dynamical Systems with the Eventual Shadowing Property

In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems with the eventual shadowing property to be mixing.     

CONSTRUCTIONS OF THE INVARIANT SETS AND INVARIANT MEASURES

In this paper, we will discuss the constructiOn problems about the invariant sets and invariant measures of continues maps~ which map complexes into themselves, using simplical approximation and Markov cbeirs. In [7], the author defined a matrix by using r-normal subdivi of the w,dimensional unit cube, considered it a Markov matrix, and constructed the invariantset and invafiant measure, In fact, the matrix he defined is not Markov matrix generally. So wewill give [7] and amendment in the last pert of this paper. We also construct an invariant set thatis the chain-recurrent set of the map by means of a non-negative matrix which only depends on themap. At hst, we will prove the higher dimension?Banach variation formuls that can simplify thetransition matrix.     

具有相交性质的近小扭转映射的不变环面的保持性

In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.     

Recurrence and decay properties of a star-typed queueing model with refusal

We consider a multiclass service system with refusal and bulk-arrival. The properties regarding recurrence, ergodicity, and decay properties of such model are discussed. The explicit criteria regarding recurrence and ergodicity are obtained. The stationary distribution is given in the ergodic case. Then, the exact value of the decay parameter, denoted by λ_E, is obtained in the transient case. The criteria for the λ_E-recurrence are also obtained. Finally, the corresponding λ_E-invariant vector/measure is considered.     

华沙圈上连续映射的某些动力性质

本文研究华沙圈上定义的连续映射的动力性质．指出对于定义在华沙圈上的连续自映射而言，有与线段自映射相应的Ｓａｒｋｏｖｓｋｉｉ定理，周期点集的闭包与回归点集的闭包相等，中心为周期点集的闭包，中心的深度不大于４，以及拓扑熵为零的充要条件是它的周期点的周期都是２的方幂．     

TML中元的明聚点和ST-1分离性

在拓扑分子格（ＴＭＬ）中引进元的明聚点概念，并讨论了聚点的性质，研究了ＳＴ_-1分离性和ＴＭＬ的明导算子．     

On translations of subsets of the real line

In this paper we discuss various questions connected with translations of subsets of the real line. Most of these questions originate from W. Sierpinski. We discuss the number of translations a single subset of the reals may have. Later we discuss almost invariant subsets of Abelian groups.

     

Recurrence and invariant measure of Markov chains in double-infinite random environments

The concepts of π -irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments. That a π -irreducible chain must be either recurrent or transient is proved, a criterion is shown for recurrent Markov chains in double-infinite random environments, the existence of invariant measure of π -irreducible chains in double-infinite environments is discussed, and then Orey’s open-questions are partially answered.     

The triangular maps with closed sets of periodic points

In a recent paper we provided a characterization of triangular maps of the square, i.e., maps given by F(x,y)=(f(x),gx(y)), satisfying condition (P1) that any chain recurrent point is periodic. For continuous maps of the interval, there is a list of 18 other conditions equivalent to (P1), including (P2) that there is no infinite ω-limit set, (P3) that the set of periodic points is closed and (P4) that any regularly recurrent point is periodic, for instance. We provide an almost complete classification among these conditions for triangular maps, improve a result given by C. Arteaga [C. Arteaga, Smooth triangular maps of the square with closed set of periodic points, J. Math. Anal. Appl. 196 (1995) 987-997] and state an open problem concerning minimal sets of the triangular maps. The paper solves partially a problem formulated by A.N. Sharkovsky in the eighties. The mentioned open problem, the validity of (P4) ⇒ (P3), is related to the question whether some regularly recurrent point lies in the fibres over an f-minimal set possessing a regularly recurrent point. We answered this question in the positive for triangular maps with nondecreasing fiber maps. Consequently, the classification is completed for monotone triangular maps.     

$C^*$-动力系统的Haagerup性质

令$A$是一个单位$C^*$-代数, $\tau$是它的一个态, $\alpha$是一个离散群$G$在$A$上保持$\tau$的作用. 首先, 我们通过考虑 $C^*$-代数的态, 推广了动力系统的Haagerup性质, 并且证明了动力系统有 Haagerup性质当且仅当它的约化交叉积有Haagerup性质. 然后, 我们引入了$G$在$A$上关于$\tau$的拟顺从作用. 最后, 利用上面的结果, 我们证明了如果$\alpha$是$G$在$A$上关于$\tau$的拟顺从作用, 那么$(A,\tau)$有Haagerup性质当且仅当$(A\rtimes_{\alpha,r}G,\tau'')$有Haagerup性质, 其中$\tau''$是由$\tau$诱导的$A\rtimes_{\alpha,r}G$上的态. 本文的主要结论推广了一些经典情况下的已知结果.     

Lattice Points Inside Rational Simplices and the Casson Invariant of Brieskorn Spheres

We express the number of lattice points inside certain simplices with vertices in Q³ or Q⁴ in terms of Dedekind–Rademacher sums. This leads to an elementary proof of a formula relating the Euler characteristic of the Seiberg–Witten-Floer homology of a Brieskorn Z-homology sphere to the Casson invariant.     

Distributional Chaos Occurring on the Set of Proper Positive Upper Banach Density Recurrent Points of One-sided Symbolic Systems

The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.     

有缺失数据的条件独立正态母体中参数的最优同变估计

在缺失数据机制是可忽略的假设下,导出了有单调缺失数据的条件独立正态模型中协方差阵和精度阵的Cholesky分解的最大似然估计和无偏估计.通过引入一类特殊的变换群并在更广义的损失下,获得了其最优同变估计.这表明最大似然估计和无偏估计是非容许的.最后,通过数值模拟验证了相关结果的有效性.