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

Akihiko Kitada, Yoshihito Ogasawara, Tomoyuki Yamamoto

    Research output: Contribution to journalArticle

    3 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 {fj 1} 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

    Fingerprint

    Self-similar Set
    Dendrite
    Zero-dimensional
    dendrites
    decomposition
    Decompose
    Homeomorphic
    contraction
    Contraction

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics

    Cite this

    On a dendrite generated by a zero-dimensional weak self-similar set. / Kitada, Akihiko; Ogasawara, Yoshihito; Yamamoto, Tomoyuki.

    In: Chaos, Solitons and Fractals, Vol. 34, No. 5, 12.2007, p. 1732-1735.

    Research output: Contribution to journalArticle

    Kitada, Akihiko ; Ogasawara, Yoshihito ; Yamamoto, Tomoyuki. / On a dendrite generated by a zero-dimensional weak self-similar set. In: Chaos, Solitons and Fractals. 2007 ; Vol. 34, No. 5. pp. 1732-1735.
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