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Dendrite maps whose every periodic point is a fixed point

Author

Listed:
  • Sun, Taixiang
  • He, Qiuli
  • Su, Dongwei
  • Xi, Hongjian

Abstract

Let D be a dendrite and f:D⟶D be a continuous map. In this note, we show: (1) Every periodic point of f is a fixed point of f if and only if fn(x) and f(x) are contained in the same connected component of D-{x} for any x∈D with f(x)≠x and any natural number n. (2) If {fn(x)}n=1∞ is convergent for any x∈D, then every periodic point of f is a fixed point of f. Besides, we construct a dendrite D and a continuous map f from D to D which every periodic point is a fixed point but {fn(x)}n=1∞ is not convergent for some x∈D.

Suggested Citation

  • Sun, Taixiang & He, Qiuli & Su, Dongwei & Xi, Hongjian, 2014. "Dendrite maps whose every periodic point is a fixed point," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 62-64.
    • Handle: RePEc:eee:chsofr:v:65:y:2014:i:c:p:62-64
    DOI: 10.1016/j.chaos.2014.04.013
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    References listed on IDEAS

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    1. Sun, Taixiang & He, Qiuli & Xi, Hongjian, 2013. "Intra-orbit separation of dense orbits of dendrite maps," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 89-92.
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