A Generalized Finite Type Condition for Iterated Function Systems

We study iterated function systems (IFS) of contractive similitudes on Rd with overlaps. We introduce a generalized finite type condition which extends the existing more restrictive condition and allows us to include IFS’s of contractive similitudes whose contraction ratios are not exponentially commensurable. We show that the generalized finite type condition implies the weak separation property. Under this condition, we can reduce the IFS to a graph-directed system and by modifying a setup of Mauldin and Williams, we can compute the Hausdorff dimension of the attractor in terms of the spectral radius of certain weighted incidence matrix.