On Limit Sets of Monotone Maps on Dendroids

Abstract

Let X be a dendrite, f : X → X be a monotone map. In the papers by I. Naghmouchi (2011, 2012) it is shown that ω-limit set ω(x, f ) of any point x ∈ X has the next properties: (1)ω(x,f)⊆Per(f)¯\omega (x,f) \subseteq \overline {Per(f)} , where Per( f ) is the set of periodic points of f ;(2)ω(x, f ) is either a periodic orbit or a minimal Cantor set.

Keywords

• dendroid
• dendrite
• monotone map
• periodic point
• non-wandering point
• ω-limit set
• 54h20
• 54f50
• 37b20
• 37c25