Abstract
In this paper, we prove that if X is a local dendrite different from the circle and \(f:X\rightarrow X\) is a continuous map then f is pointwise recurrent if and only if it is a homeomorphism such that every cut point is periodic. Meanwhile, we show in the case of dendrites that the set of almost periodic points is a continuum and equals to the union of all \(\omega \)-limit sets provided that the omega limit map is continuous and we show that it is only a necessary condition for the continuity of the omega limit map. We end the paper by suggesting some new open problems.
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The authors would like to thank the anonymous referees for their careful reading and constructive comments and suggestions.
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Askri, G., Naghmouchi, I. Pointwise Recurrence on Local Dendrites. Qual. Theory Dyn. Syst. 19, 6 (2020). https://doi.org/10.1007/s12346-020-00347-8
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DOI: https://doi.org/10.1007/s12346-020-00347-8