### 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 |
---|---|

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 1 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Chaos, solitons and fractals*,

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