Acta mathematica scientia, Series B >
LEVEL SETS AND EQUIVALENCES OF MORAN-TYPE SETS
Received date: 2015-09-16
Revised date: 2016-03-28
Online published: 2016-10-25
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).
In the paper, we consider Moran-type sets Ea given by sequences {ak
and {nk.jpg){kind=small}
. 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
Yali DU , Junjie MIAO , Min WU . LEVEL SETS AND EQUIVALENCES OF MORAN-TYPE SETS[J]. Acta mathematica scientia, Series B, 2016 , 36(5) : 1343 -1357 . DOI: 10.1016/S0252-9602(16)30073-X
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