Section: New Results

Decidability in Perturbed Dynamical Systems

Participant : Emmanuel Hainry.

We have studied the link between undecidability and robustness in dynamical systems. Indeed, undecidability occurs very easily in dynamical systems. However there exist good decision algorithms that work for most systems that are not pathological. We argue that this decidability trait may be related to their robustness to infinitesimal noise. We have proved that in smooth dynamical systems, robustness is equivalent to decidability of the reachability problem. This result relies on various hypotheses depending on the compactness of the domain and whether time is discrete or continuous [31]