A Poincar\'e--Birkhoff theorem for $C^0$-Hamiltonian maps
Symplectic Geometry
2025-06-13 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We prove a higher-dimensional version of the well-known Poincar\'e--Birkhoff theorem, using Floer homology. We also prove a relative version for Lagrangian submanifolds. The motivation is finding periodic orbits and Hamiltonian chords in the circular, restricted three-body problem.
Keywords
Cite
@article{arxiv.2506.10545,
title = {A Poincar\'e--Birkhoff theorem for $C^0$-Hamiltonian maps},
author = {Arthur Limoge and Agustin Moreno},
journal= {arXiv preprint arXiv:2506.10545},
year = {2025}
}
Comments
25 pages