Abstract
Let X be a regular curve and let f:X→X be a monotone map. In this paper, the nonwandering set of f and the structure of ω-limit (resp. α-limit) sets for f are investigated. Denote by Per(f) (resp. Ω(f)) the set of periodic points (resp. nonwandering points) of f. We show that whenever the set Per(f) is empty, then f admits a unique minimal set which is totally minimal and either a circle or a Cantor set. If Per(f) is nonempty, we show that Ω(f)=Per(f)‾. In addition, every infinite minimal set is a Cantor set which is an adding machine. On the other hand, we show that f has no Li-Yorke pairs, in particular it has zero entropy. Further results related to the equicontinuity are also obtained.
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