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Singularities of Bi-Hamiltonian Systems |
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| Authors: | Alexey Bolsinov Anton Izosimov |
| Institution: | 1. Department of Mathematical Sciences, Loughborough University, Loughborough, UK 2. Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia 3. Department of Higher Mathematics, National Research University Higher School of Economics, Moscow, Russia |
| 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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