New results on the linearization of Nambu structures

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}.Comment: 1st version, 12 page

Geometry of integrable non-Hamiltonian systems

This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the following aspects of integrable non-Hamiltonian systems: local and semi-local normal forms and associated torus actions for integrable systems, and the geometry of integrable systems of type $(n,0)$. Most of the results presented in this text are very recent, and some theorems in this text are even original in the sense that they have not been written down explicitly elsewhere.Comment: 54 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:1203.276