Let X = [0,1]^N with S = {S_1,...,S_M} a finite set of contraction maps from X to itself. A nonempty compact subset E of X is an attractor for the iterated function scheme S if E = cup_{i=1}^M S_i(E) = S(E). We show that the typical closed set in [0, 1]^N is not an attractor of any iterated function scheme.
Attractors for iterated function schemes on [0,1]^N are exceptional
D'ANIELLO, Emma
;
2015
Abstract
Let X = [0,1]^N with S = {S_1,...,S_M} a finite set of contraction maps from X to itself. A nonempty compact subset E of X is an attractor for the iterated function scheme S if E = cup_{i=1}^M S_i(E) = S(E). We show that the typical closed set in [0, 1]^N is not an attractor of any iterated function scheme.File in questo prodotto:
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