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arXiv · 1606.02605

Non-commutative integrable systems on $b$-symplectic manifolds

Anna Kiesenhofer·Eva Miranda
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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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Anna Kiesenhofer, Eva Miranda. 2016-06-08. Non-commutative integrable systems on $b$-symplectic manifolds. https://doi.org/10.1134/s1560354716060058

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