Iterated function systems with non-distinct fixed points (Q549854)

In the absence of weak separation conditions, the study of self-similar sets is by no means well understood. In this paper the author studies fractal geometry of limit sets of iterated function systems which are generated by maps which share a common fixed point. In this overlap situation he calculates the Hausdorff dimension of the limit sets for almost all contraction parameters. In fact, the Hausdorff dimension \(s\) is determined by a Hutchinson-like formula and it turns out that in the situations under consideration, the \(s\)-dimensional Hausdorff measure always vanishes.