Publications

A polynomial $f(x)$ has emergent reducibility at depth $n$ if $f^{\circ k}(x)$ is irreducible for $0 \leq k \leq n − 1$ but $f^{\circ n}(x)$ is reducible. In this paper we prove that there are infinitely many irreducible cubics $f \in \mathbb{Z}[x]$ with $f\circ f$ reducible by exhibiting a one parameter family with this property.