Fatou sets of entire solutions of linear differential equations

This paper is devoted to studying the dynamical properties of solutions of f ″ + A ( z ) f = 0 , where A ( z ) is an entire function of finite order. With some added conditions on A ( z ) , we prove that all the Fatou components of E ( z ) are simply-connected provided that E = f 1 f 2 and f 1 , f 2 are two linearly independent solutions of such equations.