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Cotangent models of integrable systems
dc.contributor.author | Miranda Galcerán, Eva |
dc.contributor.author | Kiesenhofer, Anna |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-09-20T11:44:44Z |
dc.date.available | 2016-09-20T11:44:44Z |
dc.date.issued | 2016-07 |
dc.identifier.citation | Miranda, E., Kiesenhofer, A. Cotangent models of integrable systems. "Communications in mathematical physics", Juliol 2016. |
dc.identifier.issn | 0010-3616 |
dc.identifier.uri | http://hdl.handle.net/2117/90069 |
dc.description.abstract | We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on b-Poisson/b-symplectic manifolds. The semilocal equivalence with such models uses the corresponding action-angle theorems in these settings: the theorem of Liouville–Mineur–Arnold for symplectic manifolds and an action-angle theorem for regular Liouville tori in Poisson manifolds (Laurent- Gengoux et al., IntMath Res Notices IMRN 8: 1839–1869, 2011). Our models comprise regular Liouville tori of Poisson manifolds but also consider the Liouville tori on the singular locus of a b-Poisson manifold. For this latter class of Poisson structures we define a twisted cotangent model. The equivalence with this twisted cotangent model is given by an action-angle theorem recently proved by the authors and Scott (Math. Pures Appl. (9) 105(1):66–85, 2016). This viewpoint of cotangent models provides a new machinery to construct examples of integrable systems, which are especially valuable in the b-symplectic case where not many sources of examples are known. At the end of the paper we introduce non-degenerate singularities as lifted cotangent models on b-symplectic manifolds and discuss some generalizations of these models to general Poisson manifolds. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
dc.subject.lcsh | Differential equations |
dc.title | Cotangent models of integrable systems |
dc.type | Article |
dc.subject.lemac | Equacions diferencials |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.identifier.doi | 10.1007/s00220-016-2720-x |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://link.springer.com.recursos.biblioteca.upc.edu/article/10.1007/s00220-016-2720-x |
dc.rights.access | Open Access |
local.identifier.drac | 18542918 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Miranda, E.; Kiesenhofer, A. |
local.citation.publicationName | Communications in mathematical physics |
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