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 C-n with nilpotent linear part. We show that a Gevrey-alpha vector field X with a nilpotent linear part can be reduced to a normal form of Gevrey-1 + alpha type with the use of a Gevrey-1 + alpha 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.

Jaar van publicatie:2012

Trefwoorden:normal forms, nilpotent linear part, representation theory, Gevrey normalization, Mathematics

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:1

CSS-citation score:1

Authors from:Higher Education

Toegankelijkheid:Closed