An arithmetic approach to parabolic multiplicity in complex dynamics

Xavier Buff, Valentin Huguin, Liz Vivas

When $\omega$ is a primitive $n$-th root of unity, the quadratic polynomial $F(z)=\omega z(1-z)$ and the entire map $F(z)=\omega z{\mathrm{e}}^{-z}$ both have a parabolic fixed point at $0$. T…