MCTAO - 2012

Section: Application Domains

Applications to some domains of mathematics.

Control theory (in particular thinking in terms of inputs and reachable set) has brought novel ideas and progresses to mathematics. For instance, some problems from classical calculus of variations have been revisited in terms of optimal control and Pontryagin's Maximum Principle  [55] ; also, closed geodesics for perturbed Riemannian metrics where constructed in  [58] , [59] with control techniques.

The work in progress  [45] is definitely in this line, applying techniques from control to construct some perturbations under constraints of Hamiltonian systems to solve longstanding open questions in dynamical systems. Other work by Rifford and Ruggiero [13] applied successfully geometric control techniques to obtain genericity properties for Hamiltonian systems.