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Article: Self-similar subsets of the Cantor set

TitleSelf-similar subsets of the Cantor set
Authors
Feng, De JunRao, HuiWang, Yang
KeywordsMiddle-third Cantor set
Self-similar subsets
Set of uniqueness
Ternary expansions
Issue Date2015
Citation
Advances in Mathematics, 2015, v. 281, p. 857-885 How to Cite?
DOI: http://dx.doi.org/10.1016/j.aim.2015.06.002
AbstractIn this paper, we study the following question raised by Mattila in 1998: what are the self-similar subsets of the middle-third Cantor set C? We give criteria for a complete classification of all such subsets. We show that for any self-similar subset F of C containing more than one point, every linear generating IFS of F must consist of similitudes with contraction ratios ±3-n, n ∈N. In particular, a simple criterion is formulated to characterize self-similar subsets of C with equal contraction ratio in modulus.
Persistent Identifierhttp://hdl.handle.net/10722/363207
ISSN
0001-8708
2023 Impact Factor: 1.5
2023 SCImago Journal Rankings: 2.022

 

DC FieldValueLanguage
dc.contributor.authorFeng, De Jun-
dc.contributor.authorRao, Hui-
dc.contributor.authorWang, Yang-
dc.date.accessioned2025-10-10T07:45:12Z-
dc.date.available2025-10-10T07:45:12Z-
dc.date.issued2015-
dc.identifier.citationAdvances in Mathematics, 2015, v. 281, p. 857-885-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/10722/363207-
dc.description.abstractIn this paper, we study the following question raised by Mattila in 1998: what are the self-similar subsets of the middle-third Cantor set C? We give criteria for a complete classification of all such subsets. We show that for any self-similar subset F of C containing more than one point, every linear generating IFS of F must consist of similitudes with contraction ratios ±3<sup>-n</sup>, n ∈N. In particular, a simple criterion is formulated to characterize self-similar subsets of C with equal contraction ratio in modulus.-
dc.languageeng-
dc.relation.ispartofAdvances in Mathematics-
dc.subjectMiddle-third Cantor set-
dc.subjectSelf-similar subsets-
dc.subjectSet of uniqueness-
dc.subjectTernary expansions-
dc.titleSelf-similar subsets of the Cantor set-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.aim.2015.06.002-
dc.identifier.scopuseid_2-s2.0-84931292092-
dc.identifier.volume281-
dc.identifier.spage857-
dc.identifier.epage885-
dc.identifier.eissn1090-2082-

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