Invariant circles and the order structure of periodic orbits in monotone twist maps (Q1822397)

Let f be an area preserving monotone twist map of the annulus and \(\omega\) an irrational number which is between the rotation numbers of f restricted to the boundaries. A non-Birkhoff periodic orbit is one whose iterates are ordered around the annulus differently from those of rigid rotation. The main result of the article: f has no invariant circle with rotation number \(\omega\) if and only if f has a non-Birkhoff periodic orbit whose rotation number is a convergent of \(\omega\).