Consider a one-parameter family of iterated function systems on the interval and a family of measures on the corresponding symbolic space, depending on the same parameter. There are several naturally occurring measures in this class, like invariant measures for systems with place-dependent probabilities and equilibrium measures for hyperbolic iterated function systems. Assuming that the IFS satisfies the transversality condition and the measures depend on the parameter regularly enough, we obtain results on the dimension and the absolute continuity of the projected measure for almost every parameter. The talk is based on a joint work with Károly Simon, Boris Solomyak and Adam Śpiewak.
Meeting ID: 852 4277 3200 Passcode: 103121