数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1343-1357.doi: 10.1016/S0252-9602(16)30073-X

• 论文 • 上一篇    下一篇

LEVEL SETS AND EQUIVALENCES OF MORAN-TYPE SETS

杜亚丽1, 苗俊杰2, 吴敏3   

  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
  • 收稿日期:2015-09-16 修回日期:2016-03-28 出版日期:2016-10-25 发布日期:2016-10-25
  • 通讯作者: Min WU,wumin@scut.edu.cn E-mail:wumin@scut.edu.cn
  • 作者简介:Yali DU,Duyali123@126.com;Junjie MIAO,jjmiao@math.ecnu.edu.cn
  • 基金资助:

    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).

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).

摘要:

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.

关键词: Moran-type sets, dimension function, level set, logarithmical equivalence

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

中图分类号: 

  • 28A78