Pointwise-recurrent dendrite maps

Details Pointwise-recurrent dendrite maps Pointwise-recurrent dendrite maps

2011-08-13

arxiv.org/abs/1108.2787v1

Mathematics

Dynamical Systems

Scientific paper

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).

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