Research

Current Research Topics:

• Symplectic and Poisson geometry, Lie groupoids and algebroids
• dynamical systems (mainly regular ones)
• singular foliation
• sub-riemannian geometry and geometric control theory (new research topic, in cooperation with people from LAAS)

Projets/Réseaux de recherche:

• Intégrabilité en mécanique hamiltonienne (ANR JC05_41465)
• GIMP (Geometry and Integrability in Mathematical Physics)

Publications:

Monograph:Jean-Paul Dufour and Nguyen Tien Zung, Poisson Structures and their Normal Forms, Progress in Mathematics, Vol. 242, 2005, XVI, 324 p., Hardcover, ISBN: 3-7643-7334-2. The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects, including singular foliations, Lie groupoids and Lie algebroids. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry.

Some recent articles:

• Proper groupoids and momentum maps: linearization, affinity, and convexity. Annales Sci. Ecole Norm. Sup 39 (2006), 841-869.
• (with Eva Miranda) A note on equivariant normal forms of Poisson structures. Math. Res. Lett. 13 (2006), 1000–1012.
• (with Philippe Monnier) Normal forms of vector fields on Poisson manifolds. Annales Mathématiques Blaise Pascal 13 (2006), 349–380.
• Torus actions and integrable systems. A. Bolsinov, A. Fomenko and A. Oshemkov eds., Topological Methods in the Theory of Integrable Systems, 2006.
• Convergence versus integrability in Birkhoff normal form. Annals of Maths. 161 (2005), No.1, 141-156.
• (with Eva Miranda) Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems. Ann. Sci. Ecole Norm. Sup. 37 (2004) , No. 6, 819-839.
• (with Philippe Monnier) Levi decomposition of smooth Poisson structures. J. Diff. Geom. 68 (2004), 347-395.
• Actions toriques et groupes d’automorphismes de singularités de systèmes dynamiques intégrables. C. R. Acad. Sci. Paris 336 (2003), No. 12, 1015-1020.
• Levi decomposition of analytic Poisson structures and Lie algebroids. Topology 42 (2003), No.6, 1403-1420.
• Symplectic topology of integrable Hamiltonian systems, II. Compositio Math. 138 (2003), No. 2, 125-156.

My full list of publications and preprints

My list of publications on MathSciNet

My preprints on ArXiv server