The adic systems are well known minimal dynamical systems. Here we study subsystems of them, the dynamic considered is the induced dynamic. In this talk we present a classification of these systems under bi-Lipschitz transformations. The tool used in this classification is the computation of the spectra of dimensions for Poincaré recurrences of sub-adic systems. We apply these results to study and classify the dynamic of their geometrical realizations, i.e. dynamically defined subsets of the Rauzy fractals, endowed with the induced dynamic.