On the centre and the set of ω-limit points of continuous maps on dendrites

It is well known that for dynamical systems generated by continuous maps of a graph, the centre of the dynamical system is a subset of the set of ω-limit points. s paper we provide an example of a continuous self-map f 1 of a dendrite such that ω ( f 1 ) is a proper subset of C ( f 1 ) . cond example is a continuous self-map f 2 of a dendrite having a strictly increasing sequence of ω-limit sets which is not contained in any maximal one. Again, this is impossible for continuous maps on graphs.