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

Akihiko Kitada, Yoshihito Ogasawara, Tomoyuki Yamamoto

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1732-1735
Number of pages4
JournalChaos, solitons and fractals
Volume34
Issue number5
DOIs
Publication statusPublished - 2007 Dec 1

ASJC Scopus subject areas

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

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