A higher-dimensional Poincaré–Birkhoff theorem without monotone twist
Alessandro Fonda, Antonio J. Ureña · Comptes Rendus Mathématique · 2016
We provide a simple proof for a higher-dimensional version of the Poincaré–Birkhoff theorem, which applies to Poincaré time maps of Hamiltonian systems. These maps are required neither to be close to the identity nor to have a monotone twist.