ON RECURRENCE IN DENDRITE FLOWS


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Authors

  • Hawete Hattab Umm Al-Qura University

Keywords:

Group action, dendrite, recurrent

Abstract

Consider a subgroup generated by a finite subset G that acts on
a dendrite X by transformations. (G, X) is called a flow. In this note, it was
proven that the flowing properties are equivalent:
(1) the flow (G, X) is pointwise recurrent;
(2) the flow (G, X) is almost periodic;
(3) the orbit closure relation of the flow (G, X) is closed;
(4) the flow (G, X) is equicontinuous.
Furthermore, we give a transitive flow having only two recurrent points

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Published

2024-11-18

How to Cite

Hattab, H. (2024). ON RECURRENCE IN DENDRITE FLOWS. Results in Nonlinear Analysis, 7(4), 21–25. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/353