  While the notion of chaos is well established for dynamical systems on
manifolds, it is not so for dynamical systems over discrete spaces with $ N $
variables, as binary neural networks and cellular automata. The main difficulty
is the choice of a suitable topology to study the limit $N\to\infty$. By
embedding the discrete phase space into a Cantor set we provided a natural
setting to define topological entropy and Lyapunov exponents through the
concept of error-profile. We made explicit calculations both numerical and
analytic for well known discrete dynamical models.
