Publicação: ON A CLASS OF RAUZY FRACTALS WITHOUT THE FINITENESS PROPERTY
Carregando...
Data
Autores
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.
