Common dynamics of two Pisot substitutions with the same incidence matrix | Zendy

Tarek Sellami | Zendy

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Common dynamics of two Pisot substitutions with the same incidence matrix

Author(s) -

Tarek Sellami

Publication year - 2012

Publication title -

publicationes mathematicae debrecen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.468

H-Index - 37

eISSN - 2064-2849

pISSN - 0033-3883

DOI - 10.5486/pmd.2012.5007

Subject(s) - mathematics , conjecture , unimodular matrix , intersection (aeronautics) , substitution (logic) , incidence matrix , combinatorics , matrix (chemical analysis) , fractal , incidence (geometry) , pure mathematics , computer science , mathematical analysis , geometry , materials science , composite material , structural engineering , node (physics) , engineering , programming language , aerospace engineering

International audienceThe matrix of a substitution is not sufficient to completely determine the dynamics associated, even in simplest cases since there are many words with the same abelianization. In this paper we study the common points of the canonical broken lines associated to two different Pisot irreducible substitutions $\sigma_1$ and $\sigma_2$ having the same incidence matrix. We prove that if 0 is inner point to the Rauzy fractal associated to $\sigma_1$ these common points can be generated with a substitution on an alphabet of so-called "balanced blocks"

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