微分算子的按序列分布混沌性

Distribution chaos in a sequence of differentiable operator

为了探讨微分算子动力系统的混沌性问题,对区间E=[-1,1]上的连续实函数取其绝对值的最大值作为范数,得到赋范线性空间(C(E,R),||﹒||),在(C(E,R),||﹒||)的某个解析函数子空间A上定义微分算子D及度量d,并选取A中一类特殊的解析函数Φ:E→R.在此基础上,用构造性的方法构造了D的一个按序列分布混沌集B,由此得出微分算子D是按序列分布混沌的。相对于以往对一般紧致度量空间上连续函数混沌形状的研究,本文首次具体探讨了解析函数子空间上微分算子的按序列分布混沌性,这对研究各种函数的混沌性具有一定的参考价值和指导意义。

In order to discuss the problem about the chaotic properties of the differentiable operator dynamical system, in this paper, we take the maximum of absolute value as the norm for the continuous function on the interval E = [-1, 1], and obtain the linear space （C（E, R）, ‖.‖） with norm. Define the differentiable operator D and the metric d on an analytic function subspace A of （C（E, R）, ‖.‖）, and choose a kind of special functions Ф：E→R in A. Then by constructing a distributively chaotic set B in a sequence of D we show that the differentiable operator D is distributively chaotic in a sequence. In contrast with early works on the chaotic properties of a continuous map of a compact metric space, this paper discusses the distributively chaotic properties in a sequence of the differetiable operator of an analytic function subspace. This is very useful and can offer a guide for studying the chaotic properties of all kinds of functions.