On Limit Sets of Monotone Maps on Regular Curves

• Daghar, Aymen ^[1] ; Marzougui, Habib ^[1]
  1. [1] University of Carthage

     University of Carthage

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
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  • We investigate the structure of ω-limit (resp. α-limit) sets for a monotone map f on a regular curve X. We show that for any x∈X (resp. for any negative orbit (xn)n≥0 of x), the ω-limit set ωf(x) (resp. α-limit set αf((xn)n≥0)) is a minimal set. This also holds for α-limit set αf(x) whenever x is not a periodic point. These results extend those of Naghmouchi [24] established whenever f is a homeomorphism on a regular curve and those of Abdelli [1], whenever f is a monotone map on a local dendrite. Further results related to the basin of attraction of an infinite minimal set are also obtained.