  We analyze properties of the firing map, which iterations give information
about consecutive spikes, for periodically driven linear integrate-and-fire
models. By considering locally integrable (thus in general not continuous)
input functions, we generalize some results of other authors. In particular we
prove theorems concerning continuous dependence of the firing map on the input
in suitable function spaces. Using mathematical study of the displacement
sequence of an orientation preserving circle homeomorphism, we provide also a
complete description of the regularity properties of the sequence of
interspike-intervals and behaviour of the interspike-interval distribution. Our
results allow to explain some facts concerning this distribution observed
numerically by other authors. These theoretical findings are illustrated by
carefully chosen computational examples.
