Dimensions in infinite iterated function systems consisting of bi-Lipschitz mappings

We study infinite iterated function systems (IIFSs) consisting of bi-Lipschitz mappings instead of conformal contractions, focussing on IFSs that do not satisfy the open set condition. By assuming the logarithmic distortion property and some cardinality growth condition, we obtain a formula for the Hausdorff, box, and packing dimensions of the limit set in terms of certain topological pressure. By assuming, in addition, the weak separation condition, we show that these dimensions are equal to the growth dimension of the limit set.