Pointwise-recurrent dendrite maps

Issam Naghmouchi (1)

1 Department of Mathematics

Let $D$ be a dendrite and $f:D\rightarrow D$ a continuous map. Denote by $E(D)$ and $B(D)$ the sets of endpoints and branch points of $D$ respectively. We show that if $E(D)$ is countable (resp. $B(D)$ is discrete) then $f$ is pointwise-recurrent if and only if $f$ is pointwise periodic homeomorphism (resp. every pointin $D\backslash E(D)$ is periodic).

Domaines: Systèmes dynamiques [math.DS]

Issam Naghmouchi. Pointwise-recurrent dendrite maps. 2011. ⟨hal-00614609v1⟩