New results on the linearization of Nambu structures
Differential Geometry
2012-01-12 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
In a paper with Jean-Paul Dufour in 1999 \cite{DufourZung-Nambu1999}, we gave a classification of linear Nambu structures, and obtained linearization results for Nambu structures with a nondegenerate linear part. There was a case left open in \cite{DufourZung-Nambu1999}, namely the case of smooth linearization of Nambu structures with a Type 1 hyperbolic linear part which satisfies a natural signature condition. In this paper, we will show that such hyperbolic Nambu structures are also smoothly linearizable. We will also give a strong version of the analytic linearization theorem in the analytic case, improving a result obtained in \cite{DufourZung-Nambu1999}.
Cite
@article{arxiv.1201.2219,
title = {New results on the linearization of Nambu structures},
author = {Nguyen Tien Zung},
journal= {arXiv preprint arXiv:1201.2219},
year = {2012}
}
Comments
1st version, 12 pages