A class of cubic Rauzy fractals

Autor: Ali Messaoudi, Daniel Smania, Jéfferson L.R. Bastos, Tatiana Miguel Rodrigues
Rok vydání: 2015
Předmět:
Zdroj: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.04.007
Popis: In this paper, we study arithmetical and topological properties for a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we prove the number of neighbors of ${\mathcal R}_a$ in the periodic tiling is equal to $8$. We also give explicitly an automaton that generates the boundary of ${\mathcal R}_a$. As a consequence, we prove that ${\mathcal R}_2$ is homeomorphic to a topological disk.
Databáze: OpenAIRE
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