Perturbed iterated function systems and the exact Hausdorff measure of their attractors
The author defines a perturbed iterated function system (pIFS) in \(\mathbb R^d\). Then the attractor of such a system is introduced in a similar style to that of an IFS and such a set is proved to be unique. Then a partially perturbed iterated function system (ppIFS) was defined as a perturbed IFS with a constant tail. In a setup with similitudes and the strong separation condition, the author shows that a pIFS attractor can be approximated by a sequence of ppIFS attractors in such a way that the Hausdorff measure is preserved in the limit. Last the author uses this result to calculate the exact Hausdorff measure of the pIFS attractor from that of the limiting IFS.
scientific article; zbMATH DE number 5778788