Antonio Siconolfi: Weak KAM techniques for singularly perturbed optimal control problems

We tackle singularly perturbed optimal control problems with slow and fast variables via approximation of the corresponding Hamiltonians by coercive ones. We study the latter using tools issued from weak KAM theory and transfer asymp- totically information to the original problems. In this way we recover already known facts assuming the fast variable to vary in a compact ambient, and estab- lish new results replacing compactness by suitable coercivity conditions.