Thermodynamic formalism for invariant measures in iterated function systems with overlaps

We study images of equilibrium (Gibbs) states for a class non-invertible transformations associated to conformal iterated function systems (IFSs) with overlaps [Formula: see text]. prove exact dimensionality these image measures, and find dimension formula using their overlap numbers. In particular, we obtain geometric the self-conformal measures IFSs overlaps, in terms This implies necessary sufficient condition drop. If text] is measure, then if only number Examples are also discussed.