Dimensions of a deranged Cantor set with specific contraction ratios

In-Soo Baek

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2004; 41(2): 269-274

Printed June 1, 2004

Dimensions of a deranged Cantor set with specific contraction ratios

In-Soo Baek

Pusan University of Foreign Studies

Abstract

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Abstract

We investigate a deranged Cantor set(a generalized Cantor set) using the similar method to find the dimensions of cookie-cutter repeller. That is, we will use a Gibbs measure which is a weak limit of a subsequence of discrete Borel measures to find the dimensions. The deranged Cantor set that will be considered is a generalized form of a perturbed Cantor set(a variation of the symmetric Cantor set) and a cookie-cutter repeller.

Keywords: Cantor set, fractal dimensions, Gibbs measure

MSC numbers: 28A78