Abstract

The dynamical systems arising from the tribonacci substitutions: 1 --> 12, 2 --> 13, 3 --> 1 and 1 --> 12, 2 --> 31, 3 --> 1, have very distinctive dynamical and geometrical properties. In this article Ne study the dynamics that is common to these two systems, i.e. the dynamics obtained by the product of the prefix automata of these substitutions. We show the topological properties of the geometrical realization in the plane of this symbolic space. We also show that the dynamic associated to the product automaton can be realized in the plane and on the torus as a piece exchange transformation. We discuss the generalization of these results for the k-bonacci substitutions.