Polynomial compositions with large monodromy groups and applications to arithmetic dynamics

Joachim König, Danny Neftin, Shai Rosenberg

For a composition $f=f_1\circ \cdots \circ f_r$ of polynomials $f_i\in \mathbb{Q}[x]$ of degrees $d_i\ge 5$ with alternating or symmetric monodromy group, we show that the monodromy…