Correlation dimension for self-similar Cantor sets with overlaps

K. Simon, Boris Solomyak

Research output: Contribution to journalArticle

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 language English 293-300 8 Fundamenta Mathematicae 155 3 Published - 1998

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Self-similar Set
Correlation Dimension
Cantor set
Overlap
Labeling
Express
Interval
Similarity

ASJC Scopus subject areas

• Algebra and Number Theory

Cite this

Correlation dimension for self-similar Cantor sets with overlaps. / Simon, K.; Solomyak, Boris.

In: Fundamenta Mathematicae, Vol. 155, No. 3, 1998, p. 293-300.

Research output: Contribution to journalArticle

Simon, K. ; Solomyak, Boris. / Correlation dimension for self-similar Cantor sets with overlaps. In: Fundamenta Mathematicae. 1998 ; Vol. 155, No. 3. pp. 293-300.
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