2 citations · 2 across the 4 of their papers we have counts for
6 papers
Normal forms of vector fields on Poisson manifolds
Philippe Monnier, Nguyen Tien Zung
We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.
Linearization of Poisson brackets
Rui Loja Fernandes, Philippe Monnier
We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.
A cohomology attached to a function
Philippe Monnier
In this paper, we study a certain cohomology attached to a smooth function, which arose naturally in Poisson geometry. We explain how this cohomology depends on the function, and w…
Levi decomposition for smooth Poisson structures
Philippe Monnier, Nguyen Tien Zung
We prove the existence of a local smooth Levi decomposition for smooth Poisson structures and Lie algebroids near a singular point. In the appendix of this paper, we show an abstra…
Computations of Nambu-Poisson cohomologies
Philippe Monnier
We try to generalize the Poisson cohomology of a 2-dimensional Poisson manifold to the n-vectors on a n-dimensional manifold. We define several cohomologies and we compute locally…
Poisson cohomology in dimension two
Philippe Monnier
It is known that the computation of the Poisson cohomology is closely related to the classification of singularities of Poisson structures. In this paper, we will first look for th…