### 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 |
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Pages (from-to) | 293-300 |

Number of pages | 8 |

Journal | Fundamenta Mathematicae |

Volume | 155 |

Issue number | 3 |

Publication status | Published - Dec 1 1998 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Simon, K., & Solomyak, B. (1998). Correlation dimension for self-similar Cantor sets with overlaps.

*Fundamenta Mathematicae*,*155*(3), 293-300.