On Limit Sets of Monotone Maps on Dendroids

• Autores: N. N. Makhova
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 5, Nº. 2, 2020, págs. 311-316
• Idioma: inglés
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• Resumen

  • Let X be a dendrite, f : X → X be a monotone map. In the papers by I. Naghmouchi (2011, 2012) it is shown that ω-limit set ω(x, f) of any point x ∈ X has the next properties:

    (1) ω(x, f) ⊆ Per(f), where Per(f) is the set of periodic points of f ;

    (2) ω(x, f) is either a periodic orbit or a minimal Cantor set.

    In the paper by E. Makhrova, K. Vaniukova (2016 ) it is proved that (3) Ω(f) = Per(f), where Ω(f) is the set of non-wandering points of f .

    The aim of this note is to show that the above results (1) – (3) do not hold for monotone maps on dendroids