Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems

A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families...

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Bibliographic Details
Published inPhysics letters. A Vol. 375; no. 19; pp. 1972 - 1975
Main Author Hernández-Bermejo, Benito
Format Journal Article
LanguageEnglish
Published Elsevier B.V 09.05.2011
Subjects
Atomic structure
Canonical forms
Casimir invariants
Construction
Darboux canonical form
Finite-dimensional Poisson systems
Hamiltonian systems
Jacobi identities
Reduction
Separation
Solid state physics
Hamiltonian systems
Casimir invariants
Jacobi identities
Finite-dimensional Poisson systems
Darboux canonical form
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Summary:A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. ► A new family of Poisson structures is globally characterized and analyzed. ► Such family is globally defined for arbitrary values of the dimension and the rank. ► Global construction of Casimir invariants and Darboux canonical form is provided. ► Very diverse and previously known solutions of physical interest are generalized.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2011.03.053