Equicontinuous local dendrite maps


  • Aymen Haj Salem Sfax University
  • Hawete Hattab Umm Al-Qura University
  • Tarek Rejeiba Sfax University




dendrite, equicontinuity, local dendrite, recurrent point


Let X be a local dendrite, and f : X → X be a map. Denote by E(X) the set of endpoints of X. We show that if E(X) is countable, then the following are equivalent:

(1) f is equicontinuous;

(2)  fn (X) = R(f);

(3) f|  fn (X) is equicontinuous;

(4) f| fn (X) is a pointwise periodic homeomorphism or is topologically conjugate to an irrational rotation of S 1 ;

(5) ω(x, f) = Ω(x, f) for all x ∈ X.

This result generalizes [17, Theorem 5.2], [24, Theorem 2] and [11, Theorem 2.8].


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Author Biographies

Aymen Haj Salem, Sfax University

Laboratory of Dynamical Systems and Combinatorics

Hawete Hattab, Umm Al-Qura University

Math department

Tarek Rejeiba, Sfax University

Laboratory of Dynamical Systems and Combinatorics


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How to Cite

A. H. Salem, H. Hattab, and T. Rejeiba, “Equicontinuous local dendrite maps”, Appl. Gen. Topol., vol. 22, no. 1, pp. 67–77, Apr. 2021.



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