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THE CORRELATION DIMENSION OF GENERALIZED CANTOR-LIKE SETS

  • Lee, Mi-Ryeong (Department of Mathematics, Kyungpook National University) ;
  • Baek, Hun-Ki (Department of Mathematics Education, Catholic University of Daegu)
  • Received : 2012.03.14
  • Accepted : 2012.03.29
  • Published : 2012.06.25

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.

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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