Resumen de On Limit Sets of Monotone Maps on Regular Curves

Aymen Daghar, Habib Marzougui

• 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.