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.
Original language | English (US) |
---|---|
Pages (from-to) | 507-543 |
Number of pages | 37 |
Journal | Communications in Mathematical Physics |
Volume | 331 |
Issue number | 2 |
DOIs | |
State | Published - Oct 2014 |
Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics