  By a result of Blokh from 1984, every transitive map of a tree has the
relative specification property, and so it has finite decomposition ideal,
positive entropy and dense periodic points. In this paper we construct a
transitive dendrite map with infinite decomposition ideal and a unique periodic
point. Basically, the constructed map is (with respect to any non-atomic
invariant measure) a measure-theoretic extension of the dyadic adding machine.
Together with an example of Hoehn and Mouron from 2013, this shows that
transitivity on dendrites is much more varied than that on trees.
