The common dynamics of the Tribonacci substitutions
type: Item
instance of: scholarly article
title: The common dynamics of the Tribonacci substitutions
zbMATH Open document ID: 0987.37011
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2001-05-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1103055617
review text: The author considers dynamical systems induced by the Tribonacci substitutions: \(1\to 12\), \(2\to 13\), \(3\to 1\) and \(1\to 12\), \(2\to 31\), \(3\to 1\). These substitutions have the same incidence matrix therefore the same recurrence relation, the Tribonacci recurrence relation. The fixed points of each substitution have the same digit frequencies. But they have very different dynamical and geometrical properties. The author discusses and describes the topological properties of the geometrical realization in the plane of the symbolic dynamics obtained by the product of the prefix automata of these two substitutions. Generalization concerning the \(k\)-bonacci substitutions are also discussed.
reviewed by: Andrzej Pelczar
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 37B15
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1563227
zbMATH Keywords: finite automata
zbMATH Keywords: self-similarity fractal
zbMATH Keywords: iterated functions
zbMATH Keywords: Tribonacci substitutions
zbMATH Keywords: tribonacci recurrence relation
zbMATH Keywords: symbolic dynamics
author: Víctor F. Sirvent
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1563227