Affine embeddings of Cantor sets and dimension of αβ-sets
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AbstractLet E,F ⊂ Rd be two self-similar sets, and suppose that F can be affinely embedded into E. Under the assumption that E is dust-like and has a small Hausdorff dimension, we prove the logarithmic commensurability between the contraction ratios of E and F. This gives a partial affirmative answer to Conjecture 1.2 in [9]. The proof is based on our study of the boxcounting dimension of a class of multi-rotation invariant sets on the unit circle, including the αβ-sets initially studied by Engelking and Katznelson.
Acceptance Date02/12/2016
All Author(s) ListFeng DJ, Xiong Y
Journal nameIsrael Journal of Mathematics
Year2018
Month6
Volume Number226
Issue Number2
PublisherHEBREW UNIV MAGNES PRESS
Pages805 - 826
ISSN0021-2172
eISSN1565-8511
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesMathematics;Mathematics

Last updated on 2020-05-04 at 01:44