Pointwise-recurrent dendrite maps

2011/08/13 by Naghmouchi, Issam
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1108.2787

Abstract

Let D be a dendrite and f:D-> D a continuous map. Denote by E(D) and B(D) the sets of endpoints and branch points of D respectively. We show that if E(D) is countable (resp. B(D) is discrete) then f is pointwise-recurrent if and only if f is pointwise periodic homeomorphism (resp. every pointin D\E(D) is periodic).

Related

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• Monotone Maps on dendrites and their induced maps
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• Generic chaos on dendrites
• A large class of dendrite maps for which Möbius disjointness property of Sarnak is fulfilled