Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-08T19:28:38.045Z Has data issue: false hasContentIssue false

Linearization of Nambu Structures

Published online by Cambridge University Press:  04 December 2007

JEAN-PAUL DUFOUR
Affiliation:
Départment de Mathématiques, Université Montpellier II, France
NGUYEN TIEN ZUNG
Affiliation:
Départment de Mathématiques, Université Montpellier II, France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Nambu structures are a generalization of Poisson structures in Hamiltonian dynamics, and it has been shown recently by several authors that, outside singular points, these structures are locally an exterior product of commuting vector fields. Nambu structures also give rise to co-Nambu differential forms, which are a natural generalization of integrable 1-forms to higher orders. This work is devoted to the study of Nambu tensors and co-Nambu forms near singular points. In particular, we give a classification of linear Nambu structures (integral finite-dimensional Nambu-Lie algebras), and a linearization of Nambu tensors and co-Nambu forms, under the nondegeneracy condition.

Type
Research Article
Copyright
© 1999 Kluwer Academic Publishers