### Abstract

Let S be a zero-dimensional, perfect, compact weak self-similar set generated in dendrite X by a family {f_{j}} of weak contractions from X to itself. Decomposition space D_{f} of S due to a continuous mapping f from S onto X is also a dendrite. In the dendrite D_{f}, there exists a zero-dimensional, perfect, compact weak self-similar set S^{1} based on a family {f_{j}
^{1}} each of which is topologically conjugate to f_{j}. Decomposition space D_{f1} of S^{1} due to a continuous mapping f^{1} from S^{1} onto D_{f} is again a dendrite. In this manner, through the successive formation of weak self-similar set, we can obtain a sequence X, D_{f}, D_{f1}, ... of dendrite any pair in which are mutually homeomorphic.

Original language | English |
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Pages (from-to) | 1732-1735 |

Number of pages | 4 |

Journal | Chaos, Solitons and Fractals |

Volume | 34 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2007 Dec |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

*Chaos, Solitons and Fractals*,

*34*(5), 1732-1735. https://doi.org/10.1016/j.chaos.2006.05.029

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

Research output: Contribution to journal › Article

*Chaos, Solitons and Fractals*, vol. 34, no. 5, pp. 1732-1735. https://doi.org/10.1016/j.chaos.2006.05.029

}

TY - JOUR

T1 - On a dendrite generated by a zero-dimensional weak self-similar set

AU - Kitada, Akihiko

AU - Ogasawara, Yoshihito

AU - Yamamoto, Tomoyuki

PY - 2007/12

Y1 - 2007/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34250163170&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250163170&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2006.05.029

DO - 10.1016/j.chaos.2006.05.029

M3 - Article

VL - 34

SP - 1732

EP - 1735

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 5

ER -