Emerging Topics Working Group

Abstract: Consider a completely integrable symplectic twist map of the two dimensional annulus: then the invariant curves make a partition of the annulus and they are vertically ordered by their rotation number. Here we raise a similar question in the Aubry-Mather setting. Recall that for a symplectic twist map, every Aubry-Mather set is a partial graph and has a rotation number. Elaborating on Weak KAM theory, it is possible to embed these Aubry-Mather sets in some non-invariant essential curves. We will prove that these curves fill the annulus and that that they are vertically ordered as the rotation numbers of the considered Aubry-Mather sets. This is a joint work with Maxime Zavidovique.