JournalsjfgVol. 1 , No. 3pp. 335–347

The shape of the dust-likeness locus of self-similar sets

  • Miwa Aoki

    Nara Women's University, Japan
  • Masayo Fujimura

    National Defense Academy of Japan, Yokosuka, Kanagawa, Japan
  • Masahiko Taniguchi

    Nara Women's University, Japan
The shape of the dust-likeness locus of self-similar sets cover
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Abstract

We prove that the dust-likeness locus in the deformation space of a contractive holomorphic linear iterated function systemis coincidentwith the quasiconformal deformation space. Also, we determine explicitly the dust-likeness locus restricted to several slices which are different from the Mandelbrot one, and provide specific examples that show diversity of self-similar sets.

Cite this article

Miwa Aoki, Masayo Fujimura, Masahiko Taniguchi, The shape of the dust-likeness locus of self-similar sets. J. Fractal Geom. 1 (2014), no. 3 pp. 335–347

DOI 10.4171/JFG/10