Delay differential Equations: Theory and Applications

School’s duration is two weeks (ten full days). First week will be devoted to the general theory. Three main directions will be presented : linear theory in finite and infinite dimensions ; the nonlinear case dealt with as a perturbation of the linear case ; and bifurcations from an equilibrium towards a periodic orbit. The second week will be focused on applications with, at a first place, the geometry of delay differential equations. A number of hot points will be addressed: the control of retarded systems, delays in population dynamics as well as the effect of “ noise ” on dynamical properties of delay equations.