Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774549 | Journal of Mathematical Analysis and Applications | 2017 | 6 Pages |
Abstract
We consider [0,1]N, the unit cube of RN, N⩾1. Let S={S1,â¦,SM} be a finite set of contraction maps from X to itself. A non-empty subset E of X is an attractor (or an invariant set) for the iterated function system (IFS) S if E=âªi=1MSi(E). We construct, for each sâ]0,N], a nowhere dense perfect set E contained in [0,1]N, with Hausdorff dimension s, which is not an attractor for any iterated function system composed of weak contractions from [0,1]N to itself.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Emma D'Aniello,