  In this paper we study the evolution of the wave function with the system
size in a locally periodic structure. In particular we analyse the dependence
of the wave function with the number of unit cells, which also reflects
information about its spatial behaviour in the system. We reduce the problem to
a nonlinear map and find an equivalence of its energy regions of single
periodicity and of weak chaos, with the forbidden and allowed bands of the
fully periodic system, respectively. At finite size the wave function decays
exponentially with system size, as well as in space, when the energy lies
inside a region of single periodicity, while for energies in the weak chaotic
region never decays. At the transition between those regions the wave function
still decays but in a $q$-exponential form; we found that the decay length is a
half of the mean free path, which is larger than the lattice constant.
