Flat Bi-Hamiltonian Structures and Invariant Densities

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

A bi-Hamiltonian structure is a pair of Poisson structures P, Q which are compatible, meaning that any linear combination αP+ βQ is again a Poisson structure. A bi-Hamiltonian structure (P, Q) is called flat if P and Q can be simultaneously brought to a constant form in a neighborhood of a generic point. We prove that a generic bi-Hamiltonian structure (P, Q) on an odd-dimensional manifold is flat if and only if there exists a local density which is preserved by all vector fields Hamiltonian with respect to P, as well as by all vector fields Hamiltonian with respect to Q.

Original languageEnglish (US)
Pages (from-to)1415-1427
Number of pages13
JournalLetters in Mathematical Physics
Volume106
Issue number10
DOIs
StatePublished - Oct 1 2016
Externally publishedYes

Keywords

  • bi-Hamiltonian structures
  • Casimir functions
  • invariant densities

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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