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Pointwise chain recurrent maps of the tree
Published online by Cambridge University Press: 17 April 2009
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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.
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- Copyright © Australian Mathematical Society 2004
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