Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911793931091968 |
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| author | Bramham, Barney Pirnapasov, Abror |
| author_facet | Bramham, Barney Pirnapasov, Abror |
| contents | For a symplectic isotopy on the two-dimensional disc we show that the classical spectral invariants of Viterbo [20] can be extended in a meaningful way to {\it non-compactly} supported Hamiltonians. We establish some basic properties of these extended invariants and as an application we show that Hutchings' inequality in [8] between the Calabi invariant and the mean action spectrum holds without any assumptions on the isotopy; in [8] it is assumed that the Calabi invariant is less than the rotation number (or action) on the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum Bramham, Barney Pirnapasov, Abror Symplectic Geometry Dynamical Systems For a symplectic isotopy on the two-dimensional disc we show that the classical spectral invariants of Viterbo [20] can be extended in a meaningful way to {\it non-compactly} supported Hamiltonians. We establish some basic properties of these extended invariants and as an application we show that Hutchings' inequality in [8] between the Calabi invariant and the mean action spectrum holds without any assumptions on the isotopy; in [8] it is assumed that the Calabi invariant is less than the rotation number (or action) on the boundary. |
| title | Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2403.07863 |