A Construction of Two-Dimensional Random Substitution Systems

A two-dimensional substitution is a function that maps every letter in an alphabet to a predetermined rectangular word. It is said to be rectangular-preserving if any letter can be iterated infinitely many times via the canonical concatenation to produce larger and larger rectangular words. This typ...

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المؤلفون الرئيسيون: Felipe, Bryan Ceasar L., Miro, Eden Delight P.
التنسيق: text
منشور في: Archīum Ateneo 2024
الوصول للمادة أونلاين:https://archium.ateneo.edu/mathematics-faculty-pubs/256
https://doi.org/10.1063/5.0192196
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spelling ph-ateneo-arc.mathematics-faculty-pubs-12572024-04-15T07:27:16Z A Construction of Two-Dimensional Random Substitution Systems Felipe, Bryan Ceasar L. Miro, Eden Delight P. A two-dimensional substitution is a function that maps every letter in an alphabet to a predetermined rectangular word. It is said to be rectangular-preserving if any letter can be iterated infinitely many times via the canonical concatenation to produce larger and larger rectangular words. This type of substitution is a natural generalization of the one-dimensional deterministic substitution. In this study, we construct a random generalization of the two-dimensional rectangular-preserving substitutions. In particular, we extend the notion of rectangular-preserving to two-dimensional finite-set-valued substitution, a function where every letter is assigned a finite set of nonempty rectangular words, in order to define what we call as two-dimensional rectangular-preserving random substitutions. We give a simple necessary and sufficient condition for a two-dimensional finite-set-valued substitution to be rectangular-preserving. We also define a family of one-dimensional random substitutions such that the product of any two random substitutions in this family give rise to a two-dimensional rectangular-preserving random substitution. Finally, we discuss the associated two-dimensional subshifts to rectangular-preserving random substitutions and present some dynamical properties of the corresponding systems. 2024-03-07T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/256 https://doi.org/10.1063/5.0192196 Mathematics Faculty Publications Archīum Ateneo
institution Ateneo De Manila University
building Ateneo De Manila University Library
continent Asia
country Philippines
Philippines
content_provider Ateneo De Manila University Library
collection archium.Ateneo Institutional Repository
description A two-dimensional substitution is a function that maps every letter in an alphabet to a predetermined rectangular word. It is said to be rectangular-preserving if any letter can be iterated infinitely many times via the canonical concatenation to produce larger and larger rectangular words. This type of substitution is a natural generalization of the one-dimensional deterministic substitution. In this study, we construct a random generalization of the two-dimensional rectangular-preserving substitutions. In particular, we extend the notion of rectangular-preserving to two-dimensional finite-set-valued substitution, a function where every letter is assigned a finite set of nonempty rectangular words, in order to define what we call as two-dimensional rectangular-preserving random substitutions. We give a simple necessary and sufficient condition for a two-dimensional finite-set-valued substitution to be rectangular-preserving. We also define a family of one-dimensional random substitutions such that the product of any two random substitutions in this family give rise to a two-dimensional rectangular-preserving random substitution. Finally, we discuss the associated two-dimensional subshifts to rectangular-preserving random substitutions and present some dynamical properties of the corresponding systems.
format text
author Felipe, Bryan Ceasar L.
Miro, Eden Delight P.
spellingShingle Felipe, Bryan Ceasar L.
Miro, Eden Delight P.
A Construction of Two-Dimensional Random Substitution Systems
author_facet Felipe, Bryan Ceasar L.
Miro, Eden Delight P.
author_sort Felipe, Bryan Ceasar L.
title A Construction of Two-Dimensional Random Substitution Systems
title_short A Construction of Two-Dimensional Random Substitution Systems
title_full A Construction of Two-Dimensional Random Substitution Systems
title_fullStr A Construction of Two-Dimensional Random Substitution Systems
title_full_unstemmed A Construction of Two-Dimensional Random Substitution Systems
title_sort construction of two-dimensional random substitution systems
publisher Archīum Ateneo
publishDate 2024
url https://archium.ateneo.edu/mathematics-faculty-pubs/256
https://doi.org/10.1063/5.0192196
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