A note on self-similarity in the universal sequence
type: Item
instance of: scholarly article
title: A note on self-similarity in the universal sequence
zbMATH Open document ID: 1019.37019
DOI: 10.1016/S0960-0779(97)00144-6
author: George Szpiro
published in: Chaos, Solitons and Fractals
publication date: 2000-02-15T00:00:00Z
review text: The author considers self-similarity phenomena in the universal sequences of LR-patterns which arise under analyzing the symbolic dynamics of the periodic points in one-dimensional dynamics [see \textit{N. Metropolis, M. Stein} and \textit{P. Stein}, J. Comb. Theory, Ser. A 15, 25-44 (1973; Zbl 0259.26003)]. In order to clarify the nature of this self-similarity the sequence of LR-patterns is translated into numerical values and depicted in a two-dimensional phase portrait. It is shown also that the self-similar structure of such portraits is generated by a finite number of archetypes and the number of distinct archetypes is limited to 28.
reviewed by: S. V. Zelik
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 1370432
zbMATH Keywords: maps of the interval
zbMATH Keywords: LR-patterns
zbMATH Keywords: universal sequence
MaRDI profile type: Publication
cites work: Q3908199
cites work: On finite limit sets for transformations on the unit interval
cites work: Two-dimensional cellular automata
cites work: MAP DYNAMICS OF REPRODUCTION
cites work: On the universal sequence generated by a class of unimodal functions
cites work: Statistical mechanics of cellular automata
full work available at URL: s0960-0779(97)00144-6
OpenAlex ID: W1995245757
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description: scientific article; zbMATH DE number 1370432