非自治动力系统中逐点跟踪性和极限跟踪的研究

根据离散动力系统中逐点跟踪性和极限跟踪性的定义,引入非自治动力系统中逐点跟踪性和极限跟踪性的概念,研究了非自治动力系统中逐点跟踪性和极限跟踪性的动力学性质,得到如下结果:1)若F={f_i}_i=0^∞拓扑共轭于G={g_i}_i=0^∞,则F具有逐点跟踪性当且仅当G具有逐点跟踪性;2)乘积系统(X×Y,F×G)具有逐点跟踪性当且仅当(X,F)和(Y,G)具有逐点跟踪性;3)乘积系统(X×Y,F×G)具有极限跟踪性当且仅当(X,F)和(Y,G)具有极限跟踪性.这些结果丰富了非自治动力系统中逐点跟踪性和极限跟踪性的理论.     

非自治动力系统拓扑压变分原理的一点注记

用类似于非自治熵的变分原理的方法,证明了非自治拓扑压的变分原理的一个不等式,推广了非自治熵的变分原理,丰富了非自治变分原理的内容.     

关于超空间非自治动力系统敏感依赖性的一些研究

旨在讨论非自治动力系统和其对应超空间非自治动力系统上的敏感依赖性.研究了非自治动力系统敏感依赖性和其对应超空间非自治动力系统敏感依赖性之间的蕴含关系.得到了一个使得(超空间)非自治动力系统敏感依赖性在其任意次迭代系统上得以保持的充分条件.     

非自治逆紧系统的拓扑压

主要研究了非自治逆紧系统上的拓扑压.给出了非自治逆紧系统上拓扑压的定义,得到了这种拓扑压关于集合Z的一些性质,并在同胚意义下,探讨了两个非自治逆紧系统上拓扑压的大小关系.     

非自治动力系统Bowen估计熵的变分原理

推广了经典动力系统的Bowen拓扑熵,给出了非自治动力系统的Bowen估计熵的定义,讨论了非自治动力系统的Bowen估计熵和局部估计熵的关系,推广了自治动力系统Bowen拓扑熵的Billingsley型定理,研究了非自治动力系统的Bowen α-估计熵的Billingsley型定理.此外,给出了非自治动力系统Bowen...     

Cantor极小动力系统生成交叉积C~*-代数的K_0群

设(X,α)为一个Cantor极小系统,C(X)×_αZ为相应的交叉积C~*-代数,U,V为X内的两个clopen集.证明了如果[j_α(1U)_0=[jα(1_v)]_0∈K_0(C(X)×_αZ),则存在α的一个拓扑全群元素σ,使得σ(U)=V.     

Cantor极小动力系统生成交叉积C~*-代数的K_0群

设(X,α)为一个Cantor极小系统,C(X)×_αZ为相应的交叉积C~*-代数,U,V为X内的两个clopen集.证明了如果[j_α(1_U)]_0=[j_α(1_V)]_0∈K_0(C(X)×_αZ),则存在α的一个拓扑全群元素σ,使得σ(U)=V.     

非自治无穷维动力系统的惯性流形

本文讨论非自治无穷维动力系统的解的长时间行为·在谱间隙条件成立的情况下，对一类非自治发展方程证明了惯性流形的存在性·     

KD-拉回吸引的非自治动力系统拉回吸引子的存在性及其应用

利用拉回吸引子的存在性理论,证明了具有KD-拉回吸引的非自治动力系统拉回吸引子的存在性,拉回吸引子是单点集,是不变的.对无解域上的非自治反映扩散方程,证明了拉回指数吸引子的存在性,是方程唯一拉回指数吸引的稳定解.     

非自治Klein-Gordon-Schr(o)dinger格点动力系统的一致吸引子

首先证明了耗散的非自治Klein-Gordon-Schr(o)dinger格点动力系统的解确定的一族过程的紧一致吸引子的存在性.其次得到了该紧一致吸引子的Kolmogorov熵的一个上界.最后建立了该紧一致吸引子的上半连续性.     

Chaos induced by weak A-coupled-expansion of non-autonomous discrete dynamical systems

This paper focuses on chaos induced by weak A-coupled-expansion of non-autonomous discrete systems in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, separately. A new concept of weak A-coupled-expansion for non-autonomous discrete systems, whose condition is weaker than that of A-coupled-expansion, is introduced, and several new criteria of chaos induced by weak A-coupled-expansion of non-autonomous discrete systems are established. By applying some close relationships between chaotic dynamical behaviours of the original system and its induced systems, two criteria of chaos are established. One example is provided for illustration.     

Existence of backwards-compact pullback attractors for non-autonomous lattice dynamical systems

A pullback attractor is called backward compact if the union of attractors over the past time is pre-compact. We show that this kind of attractor exists for the first-order non-autonomous lattice dynamical system when the external force is backwards tempered and backwards asymptotically tail-null.     

Chaos induced by snap-back repellers in non-autonomous discrete dynamical systems

This paper focuses on chaos induced by snap-back repellers in non-autonomous discrete systems. A new concept of snap-back repeller for non-autonomous discrete systems is introduced and several new criteria of chaos induced by snap-back repellers in non-autonomous discrete systems are established. In addition, it is proved that a regular and nondegenerate snap-back repeller in non-autonomous discrete systems implies chaos in the (strong) sense of Li–Yorke. Two illustrative examples are proved.     

Sensitivity of non-autonomous discrete dynamical systems

In this paper, the sensitivity for non-autonomous discrete systems is investigated. First of all, two sufficient conditions of sensitivity for general non-autonomous dynamical systems are presented. At the same time, one stronger form of sensitivity, that is, cofinite sensitivity, is introduced for non-autonomous systems. Two sufficient conditions of cofinite sensitivity for general non-autonomous dynamical systems are presented. We generalized the result of sensitivity and strong sensitivity for autonomous discrete systems to general non-autonomous discrete systems, and the conditions in this paper are weaker than the correlated conditions of autonomous discrete systems.     

Some problems on fractal geometry and topological dynamical systems

This paper is a continuation of [14], some new problems on fractal geometry and topological dynamical systems have been posed.     

Estimations of topological entropy for non-autonomous discrete systems

This paper is concerned with estimations of topological entropy for non-autonomous discrete systems. An estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for systems in compact metric spaces are obtained by their topological equi-semiconjugacy to subshifts of finite type under certain conditions. One example is provided for illustration.