Bilipschitz embedding of homogeneous fractals

[摘要] 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. (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Fractal;Bilipschitz embedding;Ahlfors-David regular set;Moran set