Simultaneously preperiodic points for families of polynomials in normal form

Dragos Ghioca, Liang-Chung Hsia, Khoa Dang Nguyen

Let $d>m>1$ be integers, let $c_1,\dots ,c_{m+1}$ be distinct complex numbers, and let $\mathbf{f}(z):=z^d+t_1{z}^{m-1}+t_2{z}^{m-2}+\cdots +t_{m-1}z+t_m$ be an $m$-parameter family o…