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- Title
PERTURBED ITERATED FUNCTION SYSTEMS AND THE EXACT HAUSDORFF MEASURE OF THEIR ATTRACTORS.
- Authors
Freeman, Nicholas
- Abstract
We define a perturbed iterated function system (pIFS) in Rd as, loosely speaking, a sequence of iterated function systems (IFSs) whose constituent transformations converge towards some limiting IFS. We define the attractor of such a system in a similar style to that of an IFS, and prove that such a set exists uniquely. We define a partially perturbed IFS (ppIFS) to be a perturbed IFS with a constant tail. In a setup with similitudes and the strong separation condition we show 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. We use this result to calculate the exact Hausdorff measure of the pIFS attractor from that of the limiting IFS.
- Subjects
MATHEMATICAL functions; HAUSDORFF measures; ATTRACTORS (Mathematics); PERTURBATION theory; MEASURE theory; FRACTALS; CANTOR sets
- Publication
Real Analysis Exchange, 2010, Vol 35, Issue 1, p91
- ISSN
0147-1937
- Publication type
Article
- DOI
10.14321/realanalexch.35.1.0091