Apologies if this is a vague question.

It seems that a lot of the literature in smooth dynamics is focused on understanding systems that exhibit hyperbolic/non-uniformly hyperbolic behavior. In other words, these are systems which have nonzero Lyapunov exponents on a set of positive measure. There are a variety of tools that one can use in this setting, which from my understanding often comes from the existence of local stable/unstable manifolds (e.g. notions like accessibility).

Is there a corresponding general theory/set of tools for systems with everywhere zero Lyapunov spectrum? Even a pointer to an analogous monograph such as the book on nonuniform hyperbolicity by Barreira and Pesin would be very helpful.