The effect of rational maps on polynomial maps Pierrette Cassou-Noguès (2001) Annales Polonici Mathematici We describe the polynomials P ∈ ℂ[x,y] such that P ( 1 / v ⁿ , A ₁ v ⁿ + A ₂ v 2 n + . . . + A m - 1 v n ( m - 1 ) + v n m - k w ) ∈ ℂ [ v , w ] . As applications we give new examples of bad field generators and examples of families of polynomials with smooth and irreducible fibers.