Special α -Limit Points and γ -Limit Points of a Dendrite Map

• Sun, Taixiang ^[1] ; Tang, Yalin ^[2] ; Su, Guangwang ^[1] ; Xi, Hongjian ^[1] ; Qin, Bin ^[1]
  1. [1] Guangxi University of Finance and Economics

     Guangxi University of Finance and Economics

     China

     
  2. [2] Guangxi University

     Guangxi University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 245-257
• Idioma: inglés
• DOI: 10.1007/s12346-017-0225-4
• Enlaces
  • Texto completo
• Resumen

  • Let (X, d) be a compact metric space and f be a continuous map from X to X. Denote by R(f), SA(f) and Γ(f) the set of recurrent points, the set of special α-limit points and the set of γ-limit points of f, respectively. It is well known that for an interval map f, the following three statements hold: (1) R(f)⊂SA(f)∩Γ(f); (2) SA(f)=Γ(f); (3) SA(f)∪Γ(f)⊂R(f)¯. The aim of this paper is to show that the above statement (1) holds for maps of dendrites with the number of endpoints being ℵ0 (the cardinal number of the set of positive integers) and the above statements (2) and (3) do not hold for maps of dendrites with the number of endpoints being ℵ0. Besides, we also study unilateral γ-limit points for maps of dendrites with the number of branch points being finite.

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