Tilings induced by a class of cubic Rauzy fractals

Autor(es)

Loridant, B. ^[1] ; Messaoudi, A. ^[2] ; Surer, P. ^[2] ; Thuswaldner, J. M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Leoben, Lehrstuhl Math & Stat, A-8700 Leoben - Austria

^[2] IBILCE UNESP, Dept Matemat, Sao Jose Do Rio Preto - Brazil

• Tipo de documento: Artigo Científico
• Fonte: THEORETICAL COMPUTER SCIENCE; v. 477, p. 6-31, MAR 18 2013.
• Citações Web of Science: 10

Resumo

We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated with beta-substitutions related to the polynomial x(3) - ax(2) - bx - 1 for a >= b >= 1. In particular, we compute the corresponding boundary graphs, describing the adjacencies in the tilings. These graphs are a valuable tool for more advanced studies of the topological properties of the Rauzy fractals. As an example, we show that the Rauzy fractals are not homeomorphic to a closed disc as soon as a <= 2b - 4. The methods presented in this paper may be used to obtain similar results for other classes of substitutions. (c) 2013 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 09/07744-0 - Substituições, Sistemas de Numeração e Fractais de Rauzy
• Beneficiário: Paul Surer
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado