A DICHOTOMY OF STRONG OPEN SET CONDITION OF SELF-CONFORMAL SETS

Liang-Yi Huang () and Yuan Zhang
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Liang-Yi Huang: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China
Yuan Zhang: Department of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-6

Abstract: Let K be a 𠒞1+α self-conformal set. It is well known that K satisfies the strong open set condition provided it satisfies the open set condition. A point x 𠜀 K is called a trivial point of K if {x} is a connected component of K. Let U be a strong open set for K. In this paper, we show that whether U contains a trivial point of K determines several metrical and topological properties of K, including the maximal power law property and the dimension drop of the connected part of K.

Keywords: Self-conformal Set; Strong Open Set Condition; Maximal Power Law (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501675

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