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This article is cited in 6 scientific papers (total in 6 papers)
Noncommutative Integrable Systems on $b$-symplectic Manifolds
Anna Kiesenhofera, Eva Mirandaab a Department of Mathematics, Universitat Politècnica de Catalunya,
EPSEB, Avinguda del Doctor Marañón 44–50, Barcelona, Spain
b Barcelona Graduate School of Mathematics,
Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain
Abstract:
In this paper we study noncommutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering noncommutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and prove an action-angle theorem for noncommutative integrable systems on a $b$-symplectic manifold in a neighborhood of a Liouville torus inside the critical set of the Poisson structure associated to the $b$-symplectic structure.
Keywords:
Poisson manifolds, $b$-symplectic manifolds, noncommutative integrable systems, action-angle coordinates.
Received: 08.06.2016 Accepted: 05.10.2016
Citation:
Anna Kiesenhofer, Eva Miranda, “Noncommutative Integrable Systems on $b$-symplectic Manifolds”, Regul. Chaotic Dyn., 21:6 (2016), 643–659
Linking options:
https://www.mathnet.ru/eng/rcd215 https://www.mathnet.ru/eng/rcd/v21/i6/p643
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Abstract page: | 309 | References: | 30 |
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