Affine-periodic solutions of discrete dynamical systems: Massera’s criterion, affine-periodic floquet decomposition and existence results

In this manuscript, we focus on discrete dynamical systems and propose some important results according to their affine periodic solutions. We reconsider two landmark results, namely Massera?s theorem and Floquet?s theorem, for linear discrete dynamical systems with respect to affine-periodicity. We adapt affine periodicity in Floquet?s theory in order to obtain an affine-periodic Floquet?s decomposition. We also examine the existence of (Q,T)-affine periodic solutions for certain kinds of difference systems.