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Start Over Subject iterated function system

1. Continuous dependence on parameters of certain self-affine measures, and their singularity

Creator:
Ding, Daoxin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
iterated function system, self-affine set, self-affine measure, and singularity
Language:
English
Description:
In this paper, we first prove that the self-affine sets depend continuously on the expanding matrix and the digit set, and the corresponding self-affine measures with respect to the probability weight behave in much the same way. Moreover, we obtain some sufficient conditions for certain self-affine measures to be singular.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Gradual doubling property of Hutchinson orbits

Creator:
Aimar, Hugo, Carena, Marilina, and Iaffel, Bibiana
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
metric space, doubling measure, Hausdorff-Kantorovich metric, and iterated function system
Language:
English
Description:
The classical self-similar fractals can be obtained as fixed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, both have the doubling property. We prove that the elements of Hutchinson orbits possess the doubling property except perhaps for radii which decrease to zero as the step of the iteration grows, and in this sense, we say that the doubling property of the limit is achieved gradually. We use this result to prove the uniform upper doubling property of the orbits.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public