Nguyen Tien Zung

TL;DR: In this paper, the linearization of Poisson structures is discussed.Generalities on Poisson Structures and Poisson Cohomology, Levi Decomposition, Linearization, Nambu Structures, Singular Foliations, Lie Groupoids, Lie Algebroids.

TL;DR: The classical Arnold-Liouville theorem describes the geometry of integrable Hamiltonian systems near a regular level set of the moment map as mentioned in this paper, and it can be decomposed topologically, together with the associated singular Lagrangian foliation, to a direct product of simplest (codimension 1 and codimension 2) singularities.

TL;DR: In this paper, the authors give a topological and geometrical description of focus-focus singularities of integrable Hamiltonian systems and explain why the monodromy around these singularities is non-trivial.

TL;DR: The classical Arnold-Liouville theorem describes the geometry of integrable Hamiltonian systems near a regular level set of the moment map as discussed by the authors, and it can be decomposed topologically, together with the associated singular Lagrangian foliation to a direct product of simplest (codimension 1 and codimension 2) singularities.

TL;DR: In this article, an integrable Hamiltonian system with n degrees of freedom whose first integrals are invariant under the symplectic action of a compact Lie group G is considered, and it is shown that the singular Lagrangian foliation associated to this system is symplectically equivalent, in a G-equivariant way, to the linearized foliation in a neighborhood of a singular nonsmooth non-degenerate orbit.