Nilpotent and recursive flows.
Nonlinear connections and semisprays on tangent manifolds.
Nonseparated manifolds and completely unstable flows.
Normal forms for singularities of one dimensional holomorphic vector fields.
Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part
We explore the convergence/divergence of the normal form for a singularity of a vector field on with nilpotent linear part. We show that a Gevrey- vector field with a nilpotent linear part can be reduced to a normal form of Gevrey- type with the use of a Gevrey- transformation. We also give a proof of the existence of an optimal order to stop the normal form procedure. If one stops the normal form procedure at this order, the remainder becomes exponentially small.
Normalization of Poincaré singularities via variation of constants.
We present a geometric proof of the Poincaré-Dulac Normalization Theorem for analytic vector fields with singularities of Poincaré type. Our approach allows us to relate the size of the convergence domain of the linearizing transformation to the geometry of the complex foliation associated to the vector field.
Note à propos d'un résultat de Kowada sur les flots analytiques
Note on a Poincaré map