A class of cubic Rauzy fractals - Bastos, J. [UNESP]; Messaoudi, A. [UNESP]; Rodrigues, T. [UNESP]; Smania, D. (Elsevier B.V., 2015)
In this paper, we study arithmetical and topological properties for a class of Rauzy fractals R-a given by the polynomial x(3) - ax(2) + x - 1 where a >= 2 is an integer. In particular, we prove the number of neighbors of R-a in the periodic tiling is equal to 8. We also give explicitly an automaton that generates the boundary of R-a. As a consequence, we prove that R-2 is homeomorphic to a topological disk.
Keywords: Rauzy fractals; Numeration system; Automaton; Topological properties