On $k$-summable normal forms of vector fields with one zero eigenvalue

Peter De Maesschalck, Kristian Uldall Kristiansen

In this paper, we study normal forms of analytic saddle-nodes in ${\mathbb{C}}^{n+1}$ with any Poincaré rank $k\in \mathbb{N}$. The approach and the results generalize those of Bonckae…