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math.DS2016★ 5 cited
Holomorphic normal form of nonlinear perturbations of nilpotent vector fields
Laurent Stolovitch, Freek Verstringe
We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension . Based on Belitskii's work, we know that such…
math.DS2011
Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part
P. Bonckaert, F. Verstringe
We explore the convergence/divergence of the normal form for a singularity of a vector field on $\C^n$ with nilpotent linear part. We show that a Gevrey- vector field with a…
math.DS2008
On the flat remainder in normal forms of families of analytic planar saddles
Patrick Bonckaert, Freek Verstringe
We give an explicit expression for the (finitely) flat remainder after analytic normal form reduction of a family of planar saddles of diffeomorphisms or vector fields. We distingu…