# Sharkovskii order for non-wandering points

### Maria Pires de Carvalho

Universidade do Porto, Portugal### Fernando Jorge Moreira

Universidade do Porto, Portugal

## Abstract

For a map $f:I→I$, a point $x∈I$ is periodic with period $p∈N$ if $f_{p}(x)=x$ and $f_{j}(x)=x$ for all $0<j<p$. When $f$ is continuous and $I$ is an interval, a theorem due to Sharkovskii ([1]) states that there is an order in $N$, 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 the order $⊲$ to sequences of positive integers yields a Sharkovskii-type result for non-wandering points of $f$.

## 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