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THE CORRELATION DIMENSION OF GENERALIZED CANTOR-LIKE SETS
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  • Journal title : Honam Mathematical Journal
  • Volume 34, Issue 2,  2012, pp.219-230
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2012.34.2.219
 Title & Authors
THE CORRELATION DIMENSION OF GENERALIZED CANTOR-LIKE SETS
Lee, Mi-Ryeong; Baek, Hun-Ki;
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 Abstract
In the paper, a symbolic construction is considered to define generalized Cantor-like sets. Lower and upper bounds for the correlation dimension of the sets with a regular condition are obtained with respect to a probability Borel measure. Especially, for some special cases of the sets, the exact formulas of the correlation dimension are established and we show that the correlation dimension and the Hausdorff dimension of some of them are the same. Finally, we find a condition which guarantees the positive correlation dimension of the generalized Cantor-like sets.
 Keywords
correlation dimension;generalized Cantor-like set;
 Language
English
 Cited by
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