The dynamics of monotone maps of dendrites

Monotone maps of dendrites with a countable closed set of branch points of finite order are studied. The structure of $\omega$-limit sets and of periodic and non-wandering sets is established, and it is proved that the topological entropy of monotone maps is equal to zero. It is shown that monotone maps of dendrites with a non-closed set of branch points of finite order may have properties different from those of the maps considered here.