On a dendrite generated by a zero-dimensional weak self-similar set

Akihiko Kitada, Yoshihito Ogasawara, Tomoyuki Yamamoto

研究成果: Article査読

4 被引用数 (Scopus)

抄録

Let S be a zero-dimensional, perfect, compact weak self-similar set generated in dendrite X by a family {fj} of weak contractions from X to itself. Decomposition space Df of S due to a continuous mapping f from S onto X is also a dendrite. In the dendrite Df, there exists a zero-dimensional, perfect, compact weak self-similar set S1 based on a family {fj1} each of which is topologically conjugate to fj. Decomposition space Df1 of S1 due to a continuous mapping f1 from S1 onto Df is again a dendrite. In this manner, through the successive formation of weak self-similar set, we can obtain a sequence X, Df, Df1, ... of dendrite any pair in which are mutually homeomorphic.

本文言語English
ページ(範囲)1732-1735
ページ数4
ジャーナルChaos, solitons and fractals
34
5
DOI
出版ステータスPublished - 2007 12 1

ASJC Scopus subject areas

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

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