Singularities of Bi-Hamiltonian Systems

Alexey Bolsinov, Anton Izosimov

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 languageEnglish (US)
Pages (from-to)507-543
Number of pages37
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Oct 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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