Paradigms and puzzles in the theory of dynamical systems

We will outline the main features of a framework for a theory of dynamical systems. The basic ingredients form a triptych, with the behavior of a system in the center, and behavioral equations and latent variables as side panels. We will discuss a variety of representation and parametrization problems, in particular, questions related to input/output and state models. It is shown how the interconnection of systems fits into this framework, in particular, problems of feedback control. The final issue to which we pay attention is that of system identification. It is argued that exact system identification leads to the question of computing the most powerful unfalsified model.