Periodic drives are a common tool to control physical systems, but have a limited applicability because time-dependent drives generically lead to heating. How to prevent the heating is a fundamental question with important practical implications. We address this question by analyzing a chain of coupled kicked rotors, and find two situations in which the heating rate can be arbitrarily small: (i) marginal localization, for drives with large frequencies and small amplitudes, (ii) linear stability, for initial conditions close to a fixed point. In both cases, we find that the dynamics shows universal scaling laws that allow us to distinguish localized, diffusive, and super-diffusive regimes. The marginally localized phase has common traits with recently discovered pre-thermalized phases of many-body quantum-Hamiltonian systems, but does not require quantum coherence.

We believe that our work will stimulate a large number of related theoretical studies (assessing, for example, the effects of disorder, dissipation, finite size, etc, etc), as well as future experiments (classical systems, such as coupled pendula or rotors, are easier to realize in a lab). Eventually, these works will help us to clarify the differences (if any) with many-body quantum systems, and understand better both worlds.