Techniques complexes d'étude d'E.D.O.
The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
The characteristic variety of a generic foliation
We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.
The dynamics of holomorphic maps near curves of fixed points
Let be a two-dimensional complex manifold and a holomorphic map. Let be a curve made of fixed points of , i.e. . We study the dynamics near in case acts as the identity on the normal bundle of the regular part of . Besides results of local nature, we prove that if is a globally and locally irreducible compact curve such that then there exists a point and a holomorphic -invariant curve with on the boundary which is attracted by under the action of . These results are achieved...
The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
Transversely affine and transversely projective holomorphic foliations