Journal of Differential Equations
Completely ordered invariant circles are found for the gradient of the energy flow in the state space, containing the critical sets corresponding to the Birkhoff orbits of all rotation number. In particular, these ghost circles contain the Aubry-Mather sets and map-invariant circles as completely critical sets when these exist. We give a criterion for a sequence of rational ghost circles to converge to a completely critical one.
© the author
Golé, Christophe, "Ghost Circles for Twist Maps" (1992). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.