**Preprint MA 64/2007**
## Two examples of continuous maps on dendrites

**Zdeněk Kočan, Veronika Kornecká-Kurková, Michal Málek**
For dynamical systems generated by continuous maps of a compact interval, the
centre of the dynamical system is a subset of the set of ω-limit points
which is closed. This holds even for graphs. In this paper we provide an example
of a continuous self-map *f*_{1} of a dendrite such that ω(*f*_{1}) is not
closed, and it is a proper subset of C(*f*_{1}).

The second 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. Moreover, we construct a triangular map of the square with
the same property. Again, this is impossible for continuous maps on a compact interval.