ON A CLASS OF RAUZY FRACTALS WITHOUT THE FINITENESS PROPERTY

Nenhuma Miniatura disponível

Data

2019-07-01

Orientador

Coorientador

Pós-graduação

Curso de graduação

Título da Revista

ISSN da Revista

Título de Volume

Editor

Osaka Journal Of Mathematics

Tipo

Artigo

Direito de acesso

Acesso restrito

Resumo

We present some topological and arithmetical aspects of a class of Rauzy fractals R-a,R-b related to the polynomials of the form P-a,P-b(x) = x(3) - ax(2) - bx - 1, where a and b are integers satisfying -a + 1 <= b <= -2. This class has the property that 0 lies on the boundary of R-a,R-b. We construct explicit finite automata that recognize the boundaries of these fractals. This allows to establish the number of neighbors of R-a,R-b in the tiling it generates. Furthermore, we prove that if 2a + 3b + 4 <= 0 then R-a,R-b is not homeomorphic to a topological disk. We also show that the boundary of the set R-3,R--2 is generated by two infinite iterated function systems.

Descrição

Palavras-chave

Idioma

Inglês

Como citar

Osaka Journal Of Mathematics. Toyonaka: Osaka Journal Of Mathematics, v. 56, n. 3, p. 577-599, 2019.

Itens relacionados

Financiadores