A variational approach to the study of the existence of invariant Lagrangian graphs (Q2869430)

The present work is an excellent survey on the existence of invariant Lagrangian graphs for Lagrangians and Hamiltonians of Tonelli type. If \(M\) is a manifold then a Lagrangian \(L:TM\rightarrow \mathbb{R}\) is Tonelli if it is \(C^2\), strictly convex in the fibres and superlinear in each fibre. The classical examples are the Riemannian energies, the mechanical Lagrangians and the Mañé's Lagrangians.NEWLINENEWLINEThe main topics discussed here are the Aubry-Mather theory and a weak Liouville-Arnold theorem together with its implications. The final section is devoted to minimal average actions.