TY - JOUR
T1 - Correlation dimension for self-similar Cantor sets with overlaps
AU - Simon, Károly
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
U2 - 10.4064/fm_1998_155_3_1_293_300
DO - 10.4064/fm_1998_155_3_1_293_300
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AN - SCOPUS:0032447474
SN - 0016-2736
VL - 155
SP - 293
EP - 300
JO - Fundamenta Mathematicae
JF - Fundamenta Mathematicae
IS - 3
ER -