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SEPARATION PROPERTIES FOR ITERATED FUNCTION SYSTEMS OF BOUNDED DISTORTION

Universidad Nacional de la Patagonia San Juan Bosco and Centro Nacional Patagónico, Boulevard Brown 2915 (U9120ACD), Puerto Madryn, Chubut, Argentina

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PABLO PANZONE

Departamento e Instituto de Matematica, Universidad Nacional del Sur, Av. Alem 1253, (8000) Bahia Blanca, Argentina

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https://doi.org/10.1142/S0218348X11005361Cited by:2 (Source: Crossref)

Abstract

In this paper we study a general separation property for subsystems G, whose attractor K_G is a sub-self-similar set. This is a generalization of the Lau-Ngai weak separation property for the bounded distortion case. For subsystems with positive Hausdorff measure in its similarity dimension, we characterize the subsets of K_G with positive measure where the separation property may fail. We exhibit two examples of fractal sets, one not satisfying the weak separation property and whose existence was questioned by Zerner, the other having positive Hausdorff measure in its dimension and with the separation property failing on a subset of positive measure.

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