What could be the statment of a possible generalization of Poincare Birkhoff theorem for
$M\times [0,\; 1]$ where $M$ is a compact orientable manifold?
2026-03-30 20:40:49.1774903249
A generalization of Poincare-Birkhoff theorem
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It depends on what feature and to what dimension you want to generalize. If $M=S^1$, this is very standard and is called twist maps (in fact it does not differ much from what you have in the article you have cited, as there you already have a cylinder due to periodicity of the map), otherwise there is Aubry-Mather theory, see here