Invariant manifolds, global attractors and almost periodic solutions of non-autonomous difference equations

The talk is devoted to the study of quasi-linear non-autonomous difference equations: invariant manifolds, compact global attractors, almost periodic and recurrent solutions, invariant manifolds and chaotic sets. We prove that such equations admit an invariant continuous section (an invariant manifold). Then, we obtain the conditions of the existence of a compact global attractor and characterize its structure. We give a criterion for the existence of almost periodic and recurrent solutions of the quasi-linear non-autonomous difference equations. Finally, we prove that quasi-linear difference equations with chaotic base admits a chaotic compact invariant set. The obtained results are applied while studying triangular maps: invariant manifolds, compact global attractors, almost periodic and recurrent solutions and chaotic sets.