Recurrent motions and global attractors of non-autonomous Lorenz systems

This paper is devoted to the study of dynamics of non-autonomous Lorenz systems. These systems are formulated and investigated in the context of non-autonomous dynamical systems. First, we prove that such systems admit a compact global attractor and characterize its structure. Then, we obtain conditions of convergence, under which all solutions of the non-autonomous Lorenz systems approach a point attractor. Third, we derive a criterion for existence of almost periodic, quasi-periodic, periodic, and recurrent motions. Finally, we prove a global averaging principle for non-autonomous Lorenz systems.