2004•Bulletin of the Korean Mathematical SocietyRequires access

DIMENSIONS OF A DERANGED CANTOR SET WITH SPECIFIC CONTRACTION RATIOS

In-Soo Baek

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.

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Key concepts: Cantor set, Mathematics, Cantor function, Null set, Cantor's diagonal argument, Uncountable set, Measure (data warehouse), Set (abstract data type)