descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Report , Other literature type 01 Nov 2016Embargo end date: 01 Jan 2016 English Publisher:Pleiades Publishing LtdJournal:Regular and Chaotic Dynamics, volume 21, pages 643-659 (issn: 1560-3547, eissn: 1468-4845,

Authors: Miranda Galcerán, Eva; Kiesenhofer, Anna;

doi: 10.1134/s1560354716060058 , 10.48550/arxiv.1606.02605

arXiv: http://arxiv.org/abs/1606.02605

handle: 2117/99720 , 2117/88884 , 2117/106379

Noncommutative integrable systems on b-symplectic manifolds

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Abstract

In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a $b$-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the $b$-symplectic structure.

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Keywords

Geometria diferencial, Varietats diferenciables, Poisson manifoldsb-symplectic manifoldsnoncommutative integrable systemsaction-angle coordinates, Geometry, b-symplectic manifolds, Varietats topològiques, FOS: Mathematics, Poisson manifolds, :Matemàtiques i estadística::Geometria::Geometria diferencial [Àrees temàtiques de la UPC], noncommutative integrable, Differencial, Differentiable manifolds, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial, Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids, action-angle coordinates, :Matemàtiques i estadística::Topologia::Varietats topològiques [Àrees temàtiques de la UPC], Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Varietats topològiques, Symplectic Geometry, noncommutative integrable systems, Mathematics - Symplectic Geometry, Topological manifolds, Poisson distribution, systems, Symplectic Geometry (math.SG), Poisson, Distribució de, Geometry, Differencial, :Enginyeria mecànica::Mecànica de fluids [Àrees temàtiques de la UPC]

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