A generalized Poincar\'e-Birkhoff theorem
Symplectic Geometry
2021-05-14 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We prove a generalization of the classical Poincar\'e--Birkhoff theorem for Liouville domains, in arbitrary even dimensions. This is inspired by the existence of global hypersurfaces of section for the spatial case of the restricted three-body problem (as proved by the authors in arXiv:2011.10386).
Cite
@article{arxiv.2011.06562,
title = {A generalized Poincar\'e-Birkhoff theorem},
author = {Agustin Moreno and Otto van Koert},
journal= {arXiv preprint arXiv:2011.06562},
year = {2021}
}
Comments
37 pages. Added details, fixed typos etc., as suggested by an anonymous referee. To appear in the Journal of fixed point theory and applications, Viterbo's 60th anniversary edition