Weak KAM solutions of conservative Twist maps of the annulus

When studying the dynamics of conservative Twist maps of the annulus, a first thing to look for is the presence of invariant essential circles. There may not be any and weak KAM solutions provide a more general class of objects that always exist (at all cohomology classes) and from which are deduced backward invariant sets called pseudographs.
We will explain that there exists a continuous choice of such weak KAM solutions with respect to the cohomology class. Moreover we will provide a rather precise description of how those weak KAM solutions can be constructed.