Twist Maps and Aubry-Mather Sets

@inproceedings{Katznelson2003TwistMA,
  title={Twist Maps and Aubry-Mather Sets},
  author={Y. Katznelson and Donald S. Ornstein},
  year={2003}
}
For an area-preserving twist map F of a finite annulus, we obtain “quasi-foliations” of the annulus by one-sided-F -invariant graphs of functions that are either continuous (in which case the graph is a fully invariant curve) or have countably many jump discontinuities. For each of the one-sided-invariant graphs there is a well defined (one-sided) rotation number and all the numbers between the rotation numbers associated with the boundary circles are