迭代函数系统的吸引子和OSC集

主要研究迭代函数系统的吸引子,OSC集和它们之间的关系．其中重点分析了吸引子的结构．首先分析Rd上几类迭代函数系统的吸引子结构以及它和OSC集之间的关系,然后在此基础上具体分析并得到了R上一些相关有趣的结果,同时也证明了它们的复杂性．     

迭代函数系统的吸引子的维数估计

某些迭代函数系统（ＩＦＳ）的吸引子的Ｈａｕｓｄｏｒｆ维数的经典估计通常由求解两个非线性方程的解得到．在相同条件下，本文给出了一些显式不等式估计，使经典估计是其中的特殊情形．而且某些ＩＦＳ的吸引子的维数可以通过求解满足一定条件的非线性方程而得出     

迭代函数系统的吸收子的维数估计

某些迭代函数系统（ＩＦＳ）的吸引子的Ｈａｕｓｄｏｒｆｆ维数的经典估计通常由求解两个非线性方程的解得到。要相同条件下，本文给出卫些显示不等式估计，使经典估计是其中的特殊情形，而且某些ＩＦＳ是吸引子的维数可以通过求解满足一定条件的线性方程而得出。     

进位吸引子与拓扑熵

Let M be a manifold (possibly with boundary), and f:M→M be continuous. Call a closed invariant set A包含M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system. Such an attractor A is called n-adic if the restriction flA can be topologically conjugate the n-adic system.     

一类动力系统的吸引子吸引速度的估计

本文首先建立一类无穷维动力系统的多项式吸引子的存在性及其吸引速度具有估计的抽象定理,随后将该定理运用于一类具有非局部弱阻尼、反阻尼以及次临界增长的非线性项的波方程.     

无穷迭代函数系统的遍历定理

度量空间的压缩映射的一个集合称为一个迭代函数系统．凝聚迭代函数系统可以被看成无穷迭代函数系统．研究了紧度量空间上的无穷迭代函数系统．利用Banach极限的特性和均匀压缩性,证明了紧度量空间上无穷迭代函数系统的随机迭代算法满足遍历性．于是,凝聚迭代函数系统的随机迭代算法也满足遍历性．     

负整数阶变参数复迭代系统的吸引子及其分形图

研究了一类负整数阶变参数复迭代系统的吸引子分布规律，且利用研究结果和计算机图示技术得到了相关的分形图。     

向量递归迭代函数系统及其不变测度

本文阐述了RIFS和IFS之间的关系,并对定义在一组紧空间上的向量递归迭代函数系统(VRIFS),定义了Markov算子,给出Markov算子是压缩算子的条件,描述了其不动点即广义递归迭代函数系统的不变测度.文中还给出了相应的拼贴定理.     

具有进位吸引子的区间映射

对于一个具有n-进位吸引子的区间连续映射,证明了"n不是2的方幂"是该映射具有正拓扑熵的充分条件但不是必要条件;探讨了函数方程f3(λx)=λf(x)的一类解,并证明这类解中的每一个成员都有3-进位吸引子.     

具有进位吸引子的区间映射

对于一个具有n-进位吸引子的区间连续映射,证明了：“n不是2的方幂”是该映射具有正拓扑熵的充分条件但不是必要条件；探讨了函数方程f~3(λx)=λf(x)的一类解,并证明这类解中的每一个成员都有3-进位吸引子．     

Hausdorff Measures versus Equilibrium States of Conformal Infinite Iterated Function Systems

Dealing with infinite iterated function systems we introduce and develop the ergodic theory of Hölder systems of functions similarly as in [HU] and [HMU]. In the context of conformal infinite iterated function systems we prove the volume lemma for the Hausdorff dimension of the projection onto the limit set of a shift invariant measure. This can be considered as a Billingsley type result. Our cenral goal is to demonstrate the appearance of the "singularity-absolute continuity" dichotomy for equilibrium states of Hölder systems of functions which has been observed in [PUZ,I] and [PUZ,II] (see also [DU1] and [DU2]) in the setting of rational functions of the Riemann sphere.     

Supports of Locally Linearly Independent M-Refinable Functions,Attractors of Iterated Function Systems and Tilings

This paper is devoted to a study of supports of locally linearly independent M-refinable functions by means of attractors of iterated function systems, where M is an integer greater than (or equal to) 2. For this purpose, the local linear independence of shifts of M-refinable functions is required. So we give a complete characterization for this local linear independence property by finite matrix products, strictly in terms of the mask. We do this in a more general setting, the vector refinement equations. A connection between self-affine tilings and L ₂ solutions of refinement equations without satisfying the basic sum rule is pointed out, which leads to many further problems. Several examples are provided to illustrate the general theory.     

一类NMIFS吸引子

本文给出了NMIFS(Nonlinear Markov Iterated Function System)理论与构造NMIFS吸引子的方法,讨论了一类NMIFS吸引子的平衡向量测度和“矩”的递归计算,分析了NMIFS吸引子的结构特征．研究结果表明:对于MIFS,可以通过递归方法来计算矩M(i)(i=1,2...);而对于NMIFS,因M(i)的计算依赖于M(j)(j≥i),故不能直接计算M(i),而只能计算其近似值．     

Approximate Forward Attractors of Non-Autonomous Dynamical Systems

In this paper the forward asymptotical behavior of non-autonomous dynamical systems and their attractors are investigated. Under general conditions, the authors show that every neighborhood of pullback attractor has forward attracting property.     

Type {mathcal{A}} Sets and the Attractors of Infinite Iterated Function Systems

The present paper belongs to the family of the contributions dedicated to more general iterated function systems. Namely, we consider infinite iterated function systems and cardinality problems concerning their attractors.     

Zalcman引理在随机迭代函数族动力系统中的应用

本文根据Schwick的思想,利用Zalcman引理讨论了随机迭代函数族动力系统,指出了函数族随机迭代动力系统的Fatou集和函数族衍生半群动力系统的Fatou集定义差别明显但却等价.并获得了如下正规定则,设F={f_i|f_i为C（C）上的非线性解析函数,i ∈ M},其中M为非空指标集,Σ_M={（j₁,j₂,…,j_n,…）|j_i ∈ M,i ∈ N},若对任意的指标序列σ=（j₁,j₂,…,j_n,…）∈ Σ_M,迭代序列{W_σⁿ=f_jn º f_jn-1 º … ºf_j1（z）|n ∈ N}在点z处正规,则函数族F本身在点z处正规.     

Attractors for Second Order Lattice Dynamical Systems

We consider the existence and the approximation of the global attractor for second order damped lattice dynamical systems.     

Properties of Neighborhoods of Attractors of Dynamical Systems

Mathematical Notes - The paper deals with the study of dynamical systems admitting compact attractors, which describe the behavior of trajectories of the system at infinity and play an important...     

Attractors of Weakly Asymptotically Compact Set-Valued Dynamical Systems

The existence of weak attractors is established for set-valued dynamical systems which are weakly asymptotically compact and weakly dissipative. Here weak properties mean with respect to at least one trajectory for each initial value. A condition ensuring the uniqueness of such weak attractors is given. The results are illustrated with an application involving a partial differential inclusion in bounded and unbounded domains. Mathematics Subject Classifications (2000) 34D45, 37B25, 37B75, 58C06.