On the dynamics of ϕ : x → x p + a in a local field David Adam; Youssef Fares — 2010 Actes des rencontres du CIRM Let K be a local field, a ∈ K and ϕ : x → x p + a where p denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system ( K , ϕ ) are cycles and describe the cycles of this system.