  We derive rigorous results describing the asymptotic dynamics of a discrete
time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic
techniques we show how the dynamics of membrane potential has a one to one
correspondence with sequences of spikes patterns (``raster plots''). Moreover,
though the dynamics is generically periodic, it has a weak form of initial
conditions sensitivity due to the presence of a sharp threshold in the model
definition. As a consequence, the model exhibits a dynamical regime
indistinguishable from chaos in numerical experiments.
