Generalized invariant measures for non-autonomous conformal iterated function systems

Abstract We consider Non-autonomous Conformal Iterated Function Systems (NCIFS) in the overlapping case. We focus on the parameterized families of NCIFS that satisfy the transversality condition, and give a dimension formula for the generalized invariant measure for a.e. parameter. We also give a sufficient condition that the generalized invariant measure is absolutely continuous for a.e. parameter.