Uniform Bounds on Pre-Images under Quadratic Dynamical Systems

Xander Faber, Benjamin Hutz, Patrick Ingram +4

For any elements b,c of a number field K, let G(b,c) denote the backwards orbit of b under the map f_c: C-->C given by f_c(x)=x^2+c. We prove an upper bound on the number of elemen…