Bulletin of the Australian Mathematical Society
- Bulletin of the Australian Mathematical Society / Volume 69 / Issue 01 / February 2004, pp 63-68
- Copyright © Australian Mathematical Society 2004
- DOI: http://dx.doi.org/10.1017/S0004972700034262 (About DOI), Published online: 17 April 2009
Research Article
Pointwise chain recurrent maps of the tree
Zhang Gengronga1 and Zeng Fanpinga1
a1 Department of Mathematics, Guangxi University, Nanning, Guangxi 530004, People's Republic of China
Let T be a tree, f: T → T 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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