This will be a non-technical talk. I will start by describing how Kolmogorov models dynamical systems and stationary processes so as to put them both into the same mathematical framework and some results that are made possible by this point of view.

These results lie on the chaotic side of dynamics.

On the rigid side of dynamics, I will describe the Kolmogorov-Moser twist theorem (part of KAM theory) and a generalization of that theorem.

I will discuss the very strong similarities between the stability properties of
chaotic and rigid systems.