We consider various classes of iterated function systems, such as those comprised of similarities and those satisfying the open set condition, and weakly contractive systems. Necessary properties are developed for a compact set to be an attractor for the various classes of iterated function systems. Since the Hausdorff metric space is complete, we are able to develop several results concerning typical compact sets and their invariance with respect to iterated function systems.
Attractors for classes of iterated function systems
D’Aniello, Emma
;
2019
Abstract
We consider various classes of iterated function systems, such as those comprised of similarities and those satisfying the open set condition, and weakly contractive systems. Necessary properties are developed for a compact set to be an attractor for the various classes of iterated function systems. Since the Hausdorff metric space is complete, we are able to develop several results concerning typical compact sets and their invariance with respect to iterated function systems.File in questo prodotto:
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