单峰映射允许揉搓序列的维数和测度

本文证明了单峰映射的允许揉搓序列组成的集合在符号空间∑_2中的 Hausdorff 维数为1,1维 Hausdorff 测度为零。     

p阶Feigenbaum映射

A continuous map f from the unit closed interval into itself is called a p-order Feigenbaum's map if fp(λx) = λf(x),f(O)=1 and f|[λ,1] is univallecular. In this paper, some characterizations of p order Feigenbaum's maps are discussed and the existence for both types of such maps is proven.     

周期点集为闭集的圆周自映射周期点的周期

Let S¹ denote the circle. In this paper, we show the following.Theorem. Let f: S¹→S¹ be a continuous map and suppose f has a fixed point and the set of periodic points of f is closed, then the period of each periodic point of f is a power of 2.Corollary. Let f: S¹→S¹ be a continuous map and suppose the set of periodic points of f is closed, then there exists an odd integer m such that the set of periods of periodic points of f is contained in the set {m·2ⁿ; n = 0,1,2,…}.     

A CHARACTERIZATION OF THE SOLUTIONS OF p－ORDER FEIGENBAUM＇S FUNCTIONAL EQUATION WITH TOPOLOGICAL ENTROPY 0

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拓扑熵为零且Schweizer-Smítal混沌的极小子转移

构造了具有零拓扑熵且为Schweizer-Smital混沌的极小子转移,从而证明对一般紧系统而言,正拓扑熵与发生在测度中心上的Schweizer-Smital混沌不等价.     

周期点集为非空闭集的圆周自映射

<正> 对于周期点集为闭集的线段自映射周期点的周期以及周期点集和回复点集的关系问题引起了许多人的兴趣,并得到了满意的结果.相应地,对于圆周自映射我们已在文献[4]和[5]中证明了:定理 A 设 f 为圆周到自身的连续映射,如果 degf=0,则 f 的周期点集的闭包等     

∑上的非弱几乎周期的回复点集和SS混沌集

该文对单边符号空间上的转移自映射进行了讨论,证明了在非弱几乎周期的回复点集上存在不可数的SS混沌集.     

一类非本原代换与混沌

考虑由两个符号的非本原等长代换诱导的子移位.借助黄文、叶向东得到的一个结果,给出此子移位为Li-Yorke混沌的一个等价刻画.进而通过对点的渐近性态的探索,证明了任何这样的子移位都没有Schweizer-Smital对.     

弱混合的一个等价条件

Let X be a compact metric space containing at least two points and let f ： X → X be continuous. In this paper, we introduce the notion of totally maximum sensitive （TMS, for short） and prove that f is weakly mixing if and only if it is TMS, and if X = [0, 1], then f is weakly mixing if and only if it is 2-maximum sensitive.