منابع مشابه
Notes on Rauzy Fractals
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...
متن کامل5 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...
متن کاملRauzy fractals with countable fundamental group
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.
متن کاملA class of cubic Rauzy fractals
1 Departamento de Matemática, IBILCE, UNESP-Universidade Estadual Paulista, 15054-000–São José do Rio Preto, Brazil. E-mail: [email protected] 2 Departamento de Matemática, IBILCE, UNESP-Universidade Estadual Paulista, 15054-000–São José do Rio Preto, Brazil. E-mail: [email protected] 3 Departamento de Matemática, FC, UNESP-Universidade Estadual Paulista, 17033-360–Bauru, Brazil. ...
متن کاملRauzy fractals with countable fundamental groups
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: Indagationes Mathematicae
سال: 2016
ISSN: 0019-3577
DOI: 10.1016/j.indag.2016.01.011