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Invariant circles and the order structure of periodic orbits in monotone twist maps. (English) Zbl 0618.58032

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

MSC:

37C80 Symmetries, equivariant dynamical systems (MSC2010)
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