Ghost circles for twist maps (Q1188234)

The author first defines the energy flow in the general context of monotone maps and then studies the gradient flow of the energy only in the case of twist maps. He finds completely ordered invariant circles for the gradient of the energy flow in the state space, containing the critical sets corresponding to the Birkhoff orbits of all rotation numbers. He also proves that, in particular, the ghost circles contain the Aubry-Mather sets, whenever existing. Finally, the author gives a criterion for a sequence of rational ghost circles to converge to a completely critical one.