Singularities of bi-Hamiltonian systems
Mathematical Physics
2016-08-10 v2 math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1203.3419,
title = {Singularities of bi-Hamiltonian systems},
author = {Alexey Bolsinov and Anton Izosimov},
journal= {arXiv preprint arXiv:1203.3419},
year = {2016}
}