LAUSR

Abstract Let G be a group acting by homeomorphisms on a local dendrite X with countable set of endpoints. In this paper, it is shown that any minimal set M of G is either a finite orbit, or a Cantor set or a circle. Furthermore, we prove that if G is a finitely generated group, then the flow ( G , X ) is a pointwise recurrent flow if and only if one of the following two statements holds: (1) X = S 1 , and ( G , S 1 ) is a minimal flow conjugate to an isometric flow, or to a finite cover of a proximal flow; (2) ( G , X ) is pointwise periodic.