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Title: Gradual doubling property of Hutchinson orbits (English)
Author: Aimar, Hugo
Author: Carena, Marilina
Author: Iaffei, Bibiana
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 65
Issue: 1
Year: 2015
Pages: 191-205
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: metric space
Keyword: doubling measure
Keyword: Hausdorff-Kantorovich metric
Keyword: iterated function system
MSC: 28A75
MSC: 28A78
idZBL: Zbl 06433729
idMR: MR3336033
DOI: 10.1007/s10587-015-0168-3
Date available: 2015-04-01T12:34:04Z
Last updated: 2020-07-03
Stable URL:
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