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

Taixiang Sun, Hongjian Xi

• 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 ).