Pointwise chain recurrent maps of the tree

• Published in: Bulletin of the Australian Mathematical Society Vol. 69; no. 1; pp. 63 - 68
• Main Authors: Gengrong, Zhang, Fanping, Zeng
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.02.2004
• Subjects: Chains
• ISSN: 0004-9727; 1755-1633
• DOI: 10.1017/S0004972700034262

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.