Pisot substitutions and Rauzy fractals
نویسندگان
چکیده
منابع مشابه
5 Substitutions , Rauzy fractals and tilings
This chapter focuses on multiple tilings associated with substitutive dynamical systems. We recall that a substitutive dynamical system (Xσ, S) is a symbolic dynamical system where the shift S acts on the set Xσ of infinite words having the same language as a given infinite word which is generated by powers of a primitive substitution σ. We restrict to the case where the inflation factor of the...
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Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact planar sets, where each set is the projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the fractal associated with any...
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This mini-workshop brought together researchers with diverse backgrounds and a common interest in facets of the Pisot conjecture, which relates certain properties of a substitution to dynamical properties of the associated subshift. Mathematics Subject Classification (2000): 37B10, 28A80, 37B50, 52C23. Introduction by the Organisers A substitution is a non-erasing morphism of the free monoid. S...
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An alphabet A is a finite set of letters. A word is a finite sequence of letters. Denote the set of words by A+. For a word u = u1u2 · · ·un ∈ A+, |u| is called the length of u. For each letter a, we denote by |u|a the number of occurrence of a in u. Full Shifts. Let AZ be the set of all biinfinite sequences of alphabets from A, i.e. AZ = {x = (xi)i∈Z : xi ∈ A, ∀i ∈ Z}. Consider a shifting oper...
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We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. This characterizes all countable fundamental groups for planar Rauzy fractals. We give an explicit construction relying on two operations on substitutions: symbolic splittings and conjugations by free group automorphisms.
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2001
ISSN: 1370-1444
DOI: 10.36045/bbms/1102714169