  By using a suitable Banach space on which we let the transfer operator act,
we make a detailed study of the ergodic theory of a unimodal map $f$ of the
interval in the Misiurewicz case. We show in particular that the absolutely
continuous invariant measure $\rho$ can be written as the sum of 1/square root
spikes along the critical orbit, plus a continuous background. We conclude by a
discussion of the sense in which the map $f\mapsto\rho$ may be differentiable.
