English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider germs of holomorphic vector fields at a fixed point having anilpotent linear part at that point, in dimension $n \geq 3$. Based onBelitskii's work, we know that such a vector field is formally conjugate to a(formal) normal form. We give a condition on that normal form which ensure thatthe normalizing transformation is holomorphic at the fixed point. We shall showthat this sufficient condition is a nilpotent version of Bruno's condition (A).In dimension 2, no condition is required since, according to Str{\'o}zyna-Zoladek, each such germ is holomorphically conjugate to a Takens normal form.Our proof is based on Newton's method and $\frak{sl}\_2(\BbbC)$-representations.

Holomorphic normal form of nonlinear perturbations of nilpotent vector fields