On the Structures and dimensions of Moran sets

Article

DOI: 10.1007/BF02884183

Cite this article as:
Hua, S., Rao, H., Wen, Z. et al. Sci. China Ser. A-Math. (2000) 43: 836. doi:10.1007/BF02884183

Abstract

The Moran sets and the Moran class are defined by geometric fashion that distinguishes the classical self-similar sets from the following points:
  1. (i)

    The placements of the basic sets at each step of the constructions can be arbitrary.

     
  2. (ii)

    The contraction ratios may be different at each step.

     
  3. (iii)

    The lower limit of the contraction ratios permits zero.

     

The properties of the Moran sets and Moran class are studied, and the Hausdorff, packing and upper Box-counting dimensions of the Moran sets are determined by net measure techniques. It is shown that some important properties of the self-similar sets no longer hold for Moran sets.

Keywords

Moran set net measure 

Copyright information

© Science in China Press 2000

Authors and Affiliations

  1. 1.Department of MathematicsTsinghua UniversityBeijingChina
  2. 2.Department of Mathematics and Center of Nonlinear Science, State Key Laboratory of SoftwareWuhan UniversityWuhanChina

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