Boyland, Philip L.; Hall, Glen Richard Invariant circles and the order structure of periodic orbits in monotone twist maps. (English) Zbl 0618.58032 Topology 26, 21-35 (1987). 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 \(\omega\). Reviewer: B.V.Loginov Cited in 3 ReviewsCited in 10 Documents MSC: 37C80 Symmetries, equivariant dynamical systems (MSC2010) Keywords:area preserving monotone twist map; periodic orbit; invariant circle PDFBibTeX XMLCite \textit{P. L. Boyland} and \textit{G. R. Hall}, Topology 26, 21--35 (1987; Zbl 0618.58032) Full Text: DOI