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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/117493 |
| Online Access: | https://hdl.handle.net/2117/117493 https://dx.doi.org/10.1016/j.geomphys.2018.05.013 |
| Access Level: | Open access |
| Keyword: | Differential equations Integrable systems Liouville theorem Equacions diferencials Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica |
| Summary: | 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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