'American Institute of Mathematical Sciences (AIMS)'
Abstract
International audienceIn this paper, we study almost periodic (a.p.) solutions of discrete dynamical systems. We first adapt some results on a.p. differential equations to a.p. difference equations, on the link between boundedness of solutions and existence of a.p. solutions. After, we obtain an existence result in the space of the Harmonic Synthesis for an equation At​(xt​,...,xt+p​)=0 when the dependance of A on t is a.p. and when At​ and DAt​ are uniformly Lipschitz and satisfy another condition which is exactly the extension of a simple one for the basic linear system. The main tools for that are Nonlinear Functional Analysis and the Newton method