A Poincaré-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908976493363200 |
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| author | Masci, Leonardo |
| author_facet | Masci, Leonardo |
| contents | We prove that an asymptotically linear Hamiltonian diffeomorphism of the standard symplectic vector space, which is non-degenerate and unitary at infinity and approaches its linear map at infinity quickly enough, has infinitely many periodic points, provided that it satisfies a natural twist condition inspired by the classical Poincaré-Birkhoff theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Poincaré-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms Masci, Leonardo Symplectic Geometry Dynamical Systems 37J12, 37J46, 53D40 We prove that an asymptotically linear Hamiltonian diffeomorphism of the standard symplectic vector space, which is non-degenerate and unitary at infinity and approaches its linear map at infinity quickly enough, has infinitely many periodic points, provided that it satisfies a natural twist condition inspired by the classical Poincaré-Birkhoff theorem. |
| title | A Poincaré-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms |
| topic | Symplectic Geometry Dynamical Systems 37J12, 37J46, 53D40 |
| url | https://arxiv.org/abs/2403.01855 |