Abstract. 
When a contractive map is forced by a chaotic discontinuous
system, the asymptotic response function that defines the attracting
invariant set can be highly irregular, with a dense set of
discontinuities. In this talk, I'll describe the properties of such
function in a basic example of linear real contractions forced by
(generalized) Baker's maps.

It is also natural to ask whether the invariant distributions of the
base and factor systems share the same characteristics and in
particular, whether the factor distribution of an absolutely continuous
SRB measure in the base can be absolutely continuous. I will show that
absolute continuity holds for almost every value of the factor
contraction rate.