How much can analog and hybrid systems be proved (super-)Turing

Church thesis and its variants say roughly that all reasonable models of computation do not have more power than Turing machines. In a contrapositive way, they say that any model with super-Turing power must have something unreasonable.Our aim is to discuss how much theoretical computer science can quantify this, by considering several classes of continuous time dynamical systems, and by studying how much they can be proved Turing or super-Turing.