Sharkovskii order for non-wandering points

For a map $f:I\to I$, a point $x\in I$ is periodic with period $p \in $\mathbb{N}$$if$f^p(x)=x$and$f^j(x)\not=x$forall$0<j<p$\mathrm{.}When$f$ is continuous and $I$ is an interval, a theorem due to Sharkovskii (\cite{BC}) states that there is an order in $\mathbb{N}$, say $⊲$, such that, if $f$ has a periodic point of period $p$ and $p⊲q$, then $f$ also has a periodic point of period $q$. In this work, we will see how an extension of this order $⊲$ to an ultrapower of the integer numbers yields a Sharkovskii-type result for non-wandering points of $f$.