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 dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals. 
Fan L\"u, Man-Li Lou, Zhi-Ying Wen and Li-Feng Xi
math.MG