DYNAMICAL PROPERTIES OF MONOTONE DENDRITE MAPS

Issam Naghmouchi (1)

1 Department of Mathematics

We show that for a monotone dendrite map f:D-> D, any w-limit set is either finite or a minimal Cantor set. We also prove that AP(f)=R(f)=\Lambda(f)= cl(P(f)) where cl(P(f)), AP(f), R(f) and \Lambda(f) denote the closure of the set of periodic points, almost periodic points, recurrent points and the union of all w-limit sets respectively. Moreover, we prove that the following properties are equivalent: (i) R(f)=D, (ii) cl(R(f))=D and (iii) D\End(D) is include in P(f).

Mots clés: Dendrite map; W-limit set; Minimal set; Periodic point; Transitive; Li-Yorke pair; Pointwise recurrent

Domaines: Systèmes dynamiques [math.DS]

Issam Naghmouchi. DYNAMICAL PROPERTIES OF MONOTONE DENDRITE MAPS. 2010. ⟨hal-00593321v2⟩