Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences
Mathematical Physics
2016-06-22 v1 Combinatorics
math.MP
Chaotic Dynamics
Quantitative Methods
Abstract
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
Keywords
Cite
@article{arxiv.1601.02097,
title = {Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences},
author = {Vladimir Al. Osipov},
journal= {arXiv preprint arXiv:1601.02097},
year = {2016}
}