A Poincaré--Birkhoff theorem for $C^0$-Hamiltonian maps

Abstract

We prove a higher-dimensional version of the well-known Poincaré--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.

25 pages