Bilipschitz embedding of homogeneous fractals

In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors–David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimen...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 432; no. 2; pp. 888 - 917
Main Authors Lü, Fan, Lou, Man-Li, Wen, Zhi-Ying, Xi, Li-Feng
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.12.2015
Subjects
Ahlfors–David regular set
Bilipschitz embedding
Fractal
Moran set
Fractal
Bilipschitz embedding
Ahlfors–David regular set
Moran set
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Summary:In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors–David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as the main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.07.006