Area preserving monotone twist diffeomorphisms without non-Birkhoff periodic points

Abstract

Let $f$ be an area preserving monotone twist diffeomorphism on the annulus. In this paper, we prove the equivalence of the following three conditions: (i) the ;annulus is foliated by circles invariant under $f$. (ii) any periodic point of $f$ is of Birkhoff type, and (iii) all iterations $f^{n}$ are twist diffeomorphisms.