Bulletin of the Australian Mathematical Society

Research Article

The centre and the depth of the centre of a tree map

Xiangdong Yea1

a1 Department of Mathematics USTC Hefei Anhui 230026, People's Republic of China

Let X be a tree and f be a continuous map from X into itself. Denote by P(f) and R(f) the set of periodic points and the set of recurrent points of f respectively. We show in this note that the centre is S0004972700015768_inline1 and the depth of the centre is at most 3. Furthermore we have S0004972700015768_inline2.

(Received November 24 1992)