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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/330267
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