Dimensions of multitype Moran sets with lower limit of the contractions being zero

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Zhu, Zhiyong¹  Dong, Enmei¹ 

[1] Northwest A&F Univ, Sch Sci, Yangling 712100, Shaanxi, Peoples R China

关键词: Fractal;    Multitype Moran set;    Net measure;    Dimension;   

DOI  :  10.1016/j.jmaa.2019.123699

来源: Elsevier

【 摘 要 】

Multitype Moran sets were studied by Liu and Wen (2005) [9]. Under the assumption of primitivity they proved that for any multitype Moran set E with a positive lower bounded condition on contracting ratios, dim(H) E = s(*) <= s* = dimp E = (dim) over bar (B) E, where s(*) and s* are the lower and upper pre-dimension according to the natural coverings. In this paper we permit that the lower limit of contraction ratios is zero, and study the two classes of them. For one of the two, by assuming some stronger condition than primitivity, we show that the above formula still holds. For the other, under no assumption of primitivity we prove that dims E = s(*) (resp. (dim) over bar E-B = s*) by assuming a mild condition, and show that the above formula also holds provided primitivity and these two mild conditions are satisfied. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free