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

Published 12 Jun 2025 in math.SG, math-ph, math.DS, and math.MP | (2506.10545v1)

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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