Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (5): 1343-1357.doi: 10.1016/S0252-9602(16)30073-X

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LEVEL SETS AND EQUIVALENCES OF MORAN-TYPE SETS

Yali DU1, Junjie MIAO2, Min WU3   

  1. 1. Department of Mathematics, South China University of Technology, Guangzhou 510641, China;
    2. Shanghai Key Laboratory of PMMP;Department of Mathematics, East China Normal University, Shanghai 200241, China;
    3. Department of Mathematics, South China University of Technology, Guangzhou 510641, China
  • Received:2015-09-16 Revised:2016-03-28 Online:2016-10-25 Published:2016-10-25
  • Contact: Min WU,wumin@scut.edu.cn E-mail:wumin@scut.edu.cn
  • Supported by:

    Jun Jie Miao was partially supported by NSFC (11201152), STCSM (13dz2260400) and FDPHEC (20120076120001). The author Min Wu was supported by NSFC (11371148), Fundamental Research Funds for the central Universities, scut (2012zz0073), Fundamental Research Funds for the Central Universities SCUT (D2154240) and Guangdong Natural Science Foundation (2014A030313230).

Abstract:

In the paper, we consider Moran-type sets Ea given by sequences {akand {nk. we prove that Ea may be decompose into the disjoint union of level sets. Moreover, we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.

Key words: Moran-type sets, dimension function, level set, logarithmical equivalence

CLC Number: 

  • 28A78
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