Abstract

We consider a family of minimal sequences on a 3-symbol alphabet with complexity 2n + 1, which satisfy a special combinatorial property. These sequences were originally defined by P. Arnoux and G. Rauzy in [2] as a generalization of the binary sturmian sequences. We prove that the dynamical system associated to each of these sequences of this family, can be realized as a dynamical system defined on a geodesic lamination on the hyperbolic disk. This is a generalization of the results shown in [17]. We also show some applications of these results.