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arXiv · 2506.10545

A Poincar\'e--Birkhoff theorem for $C^0$-Hamiltonian maps

Arthur Limoge·Agustin Moreno
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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.

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Arthur Limoge, Agustin Moreno. 2025-06-12. A Poincar\'e--Birkhoff theorem for $C^0$-Hamiltonian maps. https://arxiv.org/abs/2506.10545

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