  It is shown that the restriction of the action of any group with finite orbit
on the minimal sets of dendrites is equicontinuous. Consequently, we obtain
that the action of any amenable group and Thompson group on dendrite restricted
on minimal sets is equicontinuous. We further provide a class of non-amenable
groups whose action on dendrites has finite orbit. We extend also some of our
results to dendron. We further give a characterization of the set of invariant
probability measures and its extreme points.
