Affine embeddings and intersections of Cantor sets
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AbstractLet E,F?Rd be two self-similar sets. Under mild conditions, we show that F can be C1-embedded into E if and only if it can be affinely embedded into E; furthermore if F cannot be affinely embedded into E, then the Hausdorff dimension of the intersection E��f(F) is strictly less than that of F for any C1-diffeomorphism f on Rd. Under certain circumstances, we prove the logarithmic commensurability between the contraction ratios of E and F if F can be affinely embedded into E. As an application, we show that dimH E��f(F)
All Author(s) ListFeng D.-J., Huang W., Rao H.
Journal nameJournal de Mathématiques Pures et Appliquées
Year2014
Month1
Day1
Volume Number102
Issue Number6
PublisherElsevier BV
Place of PublicationNetherlands
Pages1062 - 1079
ISSN0021-7824
eISSN1776-3371
LanguagesEnglish-United Kingdom
KeywordsAffine embedding, C1-embedding, Central Cantor sets, Self-similar sets

Last updated on 2020-01-06 at 00:55