  We study images of equilibrium (Gibbs) states for a class of non-invertible
transformations associated to conformal iterated function systems with overlaps
$\mathcal S$. We prove exact dimensionality for these image measures, and find
a dimension formula using their overlap numbers.
  In particular, we obtain a geometric formula for the dimension of
self-conformal measures for iterated function systems with overlaps, in terms
of the overlap numbers. This implies a necessary and sufficient condition for
dimension drop. If $\nu = \pi_*\mu$ is a self-conformal measure, then $HD(\nu)
< \frac{h(\mu)}{|\chi(\mu)|}$ if and only if the overlap number $o(\mathcal S,
\mu) > 1$. Examples are also discussed.
