On simultaneously preperiodic points for one-parameter families of polynomials in characteristic $p$

Jungin Lee, GyeongHyeon Nam

For a field $L$ of characteristic $p$, a polynomial $f\in {\overline{\mathbb{F}}}_p[x]$ and $\hat{I}\pm ,{\hat{I}}^2\in L$, let $\mathrm{Prep}(f;\hat{I}\pm ,{\hat{I}}^2)$ be the set of all $\hat{I}»\in \overline{L}$ such t…