Some theorems on the almost-periodic solutions of discrete dynamical systems

Abstract In this paper, we are concerned with almost periodic sequences. We study various types of almost periodic sequences arising in the literature and adapt their notions to the parametric framework. Then, similarly to the continuous case, we aim to prove variational principles. These variational principles are used to obtain some structural results and some theorems of existence in a Hilbert framework. We give, in particular, a discrete version of Amerio's criterion, and adapt a known method to the discrete time case in order to get an existence result on Hilbert space. The condition we obtain allows to find a classical known condition in the case where the system is linear with constant coefficients.

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