In this paper, the concepts of chain recurrent points and ω-limiting points on real segment is generalized to metric space.

Let f be a continuous self-map of a tree T with n end points and every point of T be a chain recurrent point of f.

For a continuous map of tree or graph to itself, we show the properties that every isolated chain recurrent point is an eventually periodic point, and an isolated chain recurrent point which is not in the orbit of a critical point and has no critical point in its orbit is a periodic point.

Secondly,the pointwise recurrent Warsaw circle maps are the identity map and that h_A(fg)=h_A(gf) for each increasing sequences of positive integers A.