An estimate of the Hausdorff dimension of a weak self-similar set

Akihiko Kitada; Tetsuji Konishi; Takanobu Watanabe

doi:10.1016/S0960-0779(00)00252-6

An estimate of the Hausdorff dimension of a weak self-similar set

Akihiko Kitada^*, Tetsuji Konishi, Takanobu Watanabe

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

A method based on a system of weak contractions was proposed to evaluate the Hausdorff dimension of a self-similar set. The contraction coefficients of the proposed estimate were used to study the topological structure of the weak self-similar set. The monotone increasing function was also analyzed in the Hausdorff dimension using continuous contraction coefficients.

Original language	English
Pages (from-to)	363-366
Number of pages	4
Journal	Chaos, solitons and fractals
Volume	13
Issue number	2
DOIs	https://doi.org/10.1016/S0960-0779(00)00252-6
Publication status	Published - 2002 Feb

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

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10.1016/S0960-0779(00)00252-6

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title = "An estimate of the Hausdorff dimension of a weak self-similar set",

abstract = "A method based on a system of weak contractions was proposed to evaluate the Hausdorff dimension of a self-similar set. The contraction coefficients of the proposed estimate were used to study the topological structure of the weak self-similar set. The monotone increasing function was also analyzed in the Hausdorff dimension using continuous contraction coefficients.",

author = "Akihiko Kitada and Tetsuji Konishi and Takanobu Watanabe",

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AB - A method based on a system of weak contractions was proposed to evaluate the Hausdorff dimension of a self-similar set. The contraction coefficients of the proposed estimate were used to study the topological structure of the weak self-similar set. The monotone increasing function was also analyzed in the Hausdorff dimension using continuous contraction coefficients.

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An estimate of the Hausdorff dimension of a weak self-similar set

Abstract

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