Integrable systems and closed one forms
In the first part of this paper we revisit a classical topological theorem by Tischler (1970) and deduce a topological result about compact manifolds admitting a set of independent closed forms proving that the manifold is a fibration over a torus. As an application we reprove the Liouville theorem...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/117493 |
| Acceso en línea: | https://hdl.handle.net/2117/117493 https://dx.doi.org/10.1016/j.geomphys.2018.05.013 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations Integrable systems Liouville theorem Equacions diferencials Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica |
| Sumario: | In the first part of this paper we revisit a classical topological theorem by Tischler (1970) and deduce a topological result about compact manifolds admitting a set of independent closed forms proving that the manifold is a fibration over a torus. As an application we reprove the Liouville theorem for integrable systems asserting that the invariant sets or compact connected fibers of a regular integrable system is a torus. We give a new proof of this theorem (including the non-commutative version) for symplectic and more generally Poisson manifolds. |
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