Journal of Mathematics of Kyoto University

On the classification of self-similar sets determined by two contractions on the plane

Kiko Kawamura

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Abstract

We classify binary self-similar sets, which are compact sets determined by two contractions on the plane, into four classes from the viewpoint of functional equations. In this classification, we can not only show close relationships among functions with self-similarity but also give solutions to a few open problems in other field.

Article information

Source
J. Math. Kyoto Univ., Volume 42, Number 2 (2002), 255-286.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283870

Digital Object Identifier
doi:10.1215/kjm/1250283870

Mathematical Reviews number (MathSciNet)
MR1966837

Zentralblatt MATH identifier
1048.28004

Subjects
Primary: 39B22: Equations for real functions [See also 26A51, 26B25]
Secondary: 28A80: Fractals [See also 37Fxx] 37E99: None of the above, but in this section 39B12: Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]

Citation

Kawamura, Kiko. On the classification of self-similar sets determined by two contractions on the plane. J. Math. Kyoto Univ. 42 (2002), no. 2, 255--286. doi:10.1215/kjm/1250283870. https://projecteuclid.org/euclid.kjm/1250283870


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