TITLE: Uses for Sharkovskii's theorem
QUESTION [6 upvotes]: Sharkovskii's theorem is a fascinating result and ready to stand on its own. But is it also used somewhere? Are there other theorems that rely on it or somehow use the Sharkovskii ordering?

REPLY [2 votes]: Quoting from Thomas D Rogers, Remarks on Sharkovsky's Theorem, Rocky Mountain J. Math. 15 (1985) 565-569:
In regard to applications of Sharkovsky's theorem (difference equation
models) it is interesting that the result is sturdy to perturbations in $f$.
Block [5] shows that if $f$ has a point of period $n$, then there is a neighborhood $N$ of $f$ in $C(I)$ such that for all $g$ in $N$ and all positive integers $k$, with $k$ left of $n$ in the Sharkovsky order, $g$ has a point of period $k$. Kloeden [10] and Butler and Pianigiani [6] have related results.
[5] is L. Block, Stability of periodic orbits in theorem of Sharkovsky, Proc. Amer. Math. Soc. 81 (1981), 333-336.
[10] is  P. E. Kloeden, Chaotic difference equations are dense, Bull. Austral. Math. Soc. 15 (1976), 371-379.
[6] is  G. J. Butler and G. Pianigiani, Periodic points and chaotic functions in the unit interval, Bull. Austral. Math. Soc. 18 (1978), 255-265.