Arithmetic Dynamics around Linear Differential Equations

Abstract: We will talk about two types of dynamical systems coming from linear differential equations. The first dynamical system is defined by the coefficient sequence of a linear differential equation. We present a Skolem-Mahler-Lech type theorem on this dynamical system. The second dynamical system is defined by iterated integration of solutions of a linear differential equation. We present some stability results on the order of linear differential equations satisfied by the iterated integrals of these solutions.