符号序列和二重de Bruijn序列的小波分析
Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences
摘要：
符号序列的概念在复杂系统的研究中起着重要的作用。在工作中，我们感兴趣的超度量结构的一组循环序列自然产生的动力系统理论。为了构造分析和数值方法研究集群，我们引入了符号序列空间上的算子语言，并提出了一种基于小波分析的集群层次研究方法。证明了该方法的分析能力的推导计算公式{ \it两重德Bruijn序列}，德Bruijn序列的概念的扩展。开发的描述可能的优点也讨论了应用程序的背景下，
英文摘要：
The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach based on wavelet analysis for study of the cluster hierarchy. The analytic power of the approach is demonstrated by derivation of a formula for counting of {\it two-fold de Bruijn sequences}, the extension of the notion of de Bruijn sequences. Possible advantages of the developed description is also discussed in context of applied p
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