The Centre and the Depth of the Centre for Continuous Maps on Dendrites with Finite Branch Points

• Taixiang Sun ^[1] ; Hongjian Xi ^[1]
  1. [1] Guangxi University of Finance and Economics

     Guangxi University of Finance and Economics

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 3, 2017, págs. 697-702
• Idioma: inglés
• DOI: 10.1007/s12346-017-0251-2
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let D be a dendrite with finite branch points and f : D → D be continuous.

    Denote by R( f ) and ( f ) the set of recurrent points and the set of non-wandering points of f respectively. Let 0( f ) = D and n( f ) = ( f |n−1( f )) for all n ∈ N.

    The minimal m ∈ N ∪ {∞} such that m( f ) = m+1( f ) is called the depth of f . In this note, we show that 3( f ) = R( f ) and the depth of f is at most 3. Furthermore, we show that there exist a dendrite D with finite branch points and f ∈ C0(D) such that 3( f ) = R( f ) = 2( f ).