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Pointwise chain recurrent maps of the tree

Published online by Cambridge University Press:  17 April 2009

Zhang Gengrong  and
Zeng Fanping
Zhang Gengrong
Affiliation:
Department of Mathematics, Guangxi University, Nanning, Guangxi 530004, People's Republic of China
Zeng Fanping
Affiliation:
Department of Mathematics, Guangxi University, Nanning, Guangxi 530004, People's Republic of China
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 63 - 68
Copyright
Copyright © Australian Mathematical Society 2004

References

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