Gradual doubling property of Hutchinson orbits

Czechoslovak Mathematical Journal

Aimar¹  Hugo ² 

[1] Bibiana Iaffei, Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Departamento de Matemática (FHUC-UNL), Colectora Ruta No. 168, Pareje El Pozo, (3000) Santa Fe, Argentina;Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Departamento de Matemática (FIQ-UNL), Colectora Ruta No. 168, Pareje El Pozo, (3000) Santa Fe, Argentina

关键词: metric space;    doubling measure;    Hausdorff-Kantorovich metric;    iterated function system;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown