## Bulletin of the Australian Mathematical Society

### Pointwise chain recurrent maps of the tree

a1 Department of Mathematics, Guangxi University, Nanning, Guangxi 530004, People's Republic of China

Let T be a tree, f: TT be a continuous map. We show that if f is pointwise chain recurrent (that is, every point of T is chain recurrent under f), then either fan is identity or fan is turbulent if Fix(f) End(T) = or else fan−1 is identity or fan−1 is turbulent if Fix(f) End(T) ≠  . Here n denotes the number of endpoints of T and, an denotes the minimal common multiple of 2,3,…,n.

(Received June 02 2003)

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