A Poincaré--Birkhoff theorem for $C^0$-Hamiltonian maps
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916791927701504 |
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| author | Limoge, Arthur Moreno, Agustin |
| author_facet | Limoge, Arthur Moreno, Agustin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Poincaré--Birkhoff theorem for $C^0$-Hamiltonian maps Limoge, Arthur Moreno, Agustin Symplectic Geometry Mathematical Physics Dynamical Systems 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. |
| title | A Poincaré--Birkhoff theorem for $C^0$-Hamiltonian maps |
| topic | Symplectic Geometry Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2506.10545 |