### 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 - 1998 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Fundamenta Mathematicae*,

*155*(3), 293-300.

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

Research output: Contribution to journal › Article

*Fundamenta Mathematicae*, vol. 155, no. 3, pp. 293-300.

}

TY - JOUR

T1 - Correlation dimension for self-similar Cantor sets with overlaps

AU - Simon, K.

AU - Solomyak, Boris

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032447474&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032447474&partnerID=8YFLogxK

M3 - Article

VL - 155

SP - 293

EP - 300

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

SN - 0016-2736

IS - 3

ER -