Parametrization for a class of Rauzy Fractal

2014/09/03 by Bastos, Jefferson, Rodrigues, Tatiana
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.1168

Abstract

In this paper, we study a class of Rauzy fractals \mathcal R_a given by the polynomial x³- ax²+x-1 where a ≥ 2 is an integer. In particular we give explicitly an automaton that generates the boundary of \mathcal R_a and using an exotic numeration system we prove that \mathcal R_a is homeomorphic to a topological disk.

Related

• A class of cubic Rauzy Fractals
• On a class of Rauzy fractals without the finiteness property
• Boundary of the Rauzy fractal sets in \RR × \CC generated by P(x)=x⁴-x³-x²-x-1
• Topological properties of a class of cubic Rauzy fractals
• A Rauzy fractal unbounded in all directions of the plane