On Limit Sets of Monotone Maps on Regular Curves

We investigate the structure of \(\omega \)-limit (resp. \(\alpha \)-limit) sets for a monotone map f on regular curve X. show that any \(x\in X\) negative orbit \((x_{n})_{n\ge 0}\) x), set _{f}(x)\) _{f}((x_{n})_{n\ge 0})\)) is minimal set. This also holds whenever x not periodic point. These results extend those Naghmouchi [24] established homeomorphism and Abdelli [1], local dendrite. Further related to basin attraction an infinite are obtained.