Symplectic and inverse spectral geometry of integrable systems: A glimpse and open problems
We first give a glimpse of finite dimensional classical integrable Hamiltonian systems from the point of view of symplectic geometry and briefly discuss their quantum counterparts, with an emphasis on recent progress on inverse spectral geometry. Then we propose several open problems about the geome...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/131018 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/131018 |
| Access Level: | acceso abierto |
| Palabra clave: | Integrable system Symplectic manifold Hamiltonian system Spectral Eigenvalue Open problem Momentum map Toric system Semitoric system Delzant polytope Moduli space Matemáticas (Matemáticas) 12 Matemáticas |
| Sumario: | We first give a glimpse of finite dimensional classical integrable Hamiltonian systems from the point of view of symplectic geometry and briefly discuss their quantum counterparts, with an emphasis on recent progress on inverse spectral geometry. Then we propose several open problems about the geometry, topology and dynamics of these systems. The problems are largely motivated by the works of a number of authors, including Arnold, Atiyah, Colin de Verdière, Delzant, Duistermaat, Eliasson, Fomenko, Guillemin, Kolmogorov, Kostant, Moser and Sternberg. |
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