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dc.contributor.authorMiranda Galcerán, Eva
dc.contributor.authorCardona, Robert
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2022-04-11T11:45:04Z
dc.date.available2022-04-11T11:45:04Z
dc.date.issued2021-02-03
dc.identifier.citationMiranda, E.; Cardona, R. Integrable systems on singular symplectic manifolds: from local to global. 2021.
dc.identifier.otherhttps://arxiv.org/abs/2007.10314
dc.identifier.urihttp://hdl.handle.net/2117/365678
dc.description.abstractIn this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes either to infinity or to zero transversally, yielding either a b-symplectic form or a folded symplectic form. The hypersurface where the form degenerates is called critical set. We give a new impulse to the investigation of the existence of action-angle coordinates for these structures initiated in [36] and [37] by proving an action-angle theorem for folded symplectic integrable systems. Contrary to expectations, the action-angle coordinate theorem for folded symplectic manifolds cannot be presented as a cotangent lift as done for symplectic and bsymplectic forms in [36]. Global constructions of integrable systems are provided and obstructions for the global existence of action-angle coordinates are investigated in both scenarios. The new topological obstructions found emanate from the topology of the critical set Z of the singular symplectic manifold. The existence of these obstructions in turn implies the existence of singularities for the integrable system on Z.
dc.description.sponsorshipRobert Cardona acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445). Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2016. Both authors are supported by the grants reference number 2017SGR932 (AGAUR) and PID2019-103849GB-I00 / AEI / 10.13039/501100011033.
dc.format.extent34 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
dc.subject.lcshSymplectic geometry
dc.subject.lcshDynamical systems
dc.subject.otherSymplectic Geometry
dc.subject.otherMathematical Physics
dc.subject.otherDifferential Geometry
dc.subject.otherDynamical Systems
dc.subject.otherIntegrable systems
dc.subject.otherSymplectic structures
dc.titleIntegrable systems on singular symplectic manifolds: from local to global
dc.typeExternal research report
dc.subject.lemacGeometria simplèctica
dc.subject.lemacSistemes dinàmics diferenciables
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.subject.amsClassificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory
dc.rights.accessOpen Access
local.identifier.drac32416080
dc.description.versionPreprint
local.citation.authorMiranda, E.; Cardona, R.


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