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Equicontinuity of maps on dendrites

Author

Listed:
  • Camargo, Javier
  • Rincón, Michael
  • Uzcátegui, Carlos

Abstract

Given a dendrite X and a continuous map f: X → X, we show the following are equivalent: (i) ωf is continuous and Per(f)¯=⋂n∈Nfn(X); (ii) ω(x,f)=Ω(x,f) for each x ∈ X; and (iii) f is equicontinuous. Furthermore, we present some examples illustrating our results.

Suggested Citation

  • Camargo, Javier & Rincón, Michael & Uzcátegui, Carlos, 2019. "Equicontinuity of maps on dendrites," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 1-6.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:1-6
    DOI: 10.1016/j.chaos.2019.05.033
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    References listed on IDEAS

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    1. Sun, Taixiang & Chen, Zhanhe & Liu, Xinhe & Xi, Hongjian, 2014. "Equicontinuity of dendrite maps," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 10-13.
    2. Banks, John, 2005. "Chaos for induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 681-685.
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