Correlation dimension for self-similar Cantor sets with overlaps

Károly Simon, Boris Solomyak

Research output: Article

7 Citations (Scopus)

Abstract

We consider self-similar Cantor sets Λ ⊂ ℝ which are either homogeneous and Λ - Λ is an interval, or not homogeneous but having thickness greater than one. We have a natural labeling of the points of Λ which comes from its construction. In case of overlaps among the cylinders of Λ, there are some "bad" pairs (τ, ω) of labels such that τ and ω label the same point of Λ. We express how much the correlation dimension of Λ is smaller than the similarity dimension in terms of the size of the set of "bad" pairs of labels.

Original languageEnglish
Pages (from-to)293-300
Number of pages8
JournalFundamenta Mathematicae
Volume155
Issue number3
Publication statusPublished - dec. 1 1998

ASJC Scopus subject areas

  • Algebra and Number Theory

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