Sharkovskii order for non-wandering points

  • Maria Pires de Carvalho

    Universidade do Porto, Portugal
  • Fernando Jorge Moreira

    Universidade do Porto, Portugal


For a map f ⁣:IIf\colon I \rightarrow I, a point xIx \in I is periodic with period pNp \in \mathbb{N} if fp(x)=xf^p(x)=x and fj(x)xf^j(x)\not=x for all 0<j<p0<j<p. When ff is continuous and II is an interval, a theorem due to Sharkovskii ([1]) states that there is an order in N\mathbb{N}, say \lhd, such that if ff has a periodic point of period pp and pqp \lhd q, then ff also has a periodic point of period qq. In this work, we will see how an extension of the order \lhd to sequences of positive integers yields a Sharkovskii-type result for non-wandering points of ff.

Cite this article

Maria Pires de Carvalho, Fernando Jorge Moreira, Sharkovskii order for non-wandering points. Port. Math. 69 (2012), no. 2, pp. 159–165

DOI 10.4171/PM/1911