New results on the linearization of Nambu structures
Abstract
In a paper with Jean-Paul Dufour in 1999 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 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 DufourZung-Nambu1999.
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