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arXiv · 1203.3419

Singularities of bi-Hamiltonian systems

Alexey Bolsinov·Anton Izosimov
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Abstract

We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with a fixed 2-cocycle. In terms of such linearizations, we give a criterion for non-degeneracy of singular points of bi-Hamiltonian systems and describe their types.

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Alexey Bolsinov, Anton Izosimov. 2013-05-31. Singularities of bi-Hamiltonian systems. https://doi.org/10.1007/s00220-014-2048-3

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