Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 42, Number 2 (2002), 255-286.
On the classification of self-similar sets determined by two contractions on the plane
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.
J. Math. Kyoto Univ., Volume 42, Number 2 (2002), 255-286.
First available in Project Euclid: 14 August 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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