Analytic classification of 1-resonant \((\mathbb C^ n, 0)\) vector fields. (Classification analytique de champs de vecteurs 1-résonnants de \((\mathbb C^ n,0)\).) (French) Zbl 0852.58013

Stolovitch, Laurent

Asymptotic Anal. 12, No. 2, 91-143 (1996).

The vector fields studied in this paper have linear part with non-zero diagonal. A normal form is described and it is shown that under certain hypotheses fields formally equivalent to the normal form may be classified by the first cohomology of a cover of the circle with coefficients in a certain asymptotic sheaf. The chapters of the paper cover cohomological preliminaries, sectorial linearisation of systems with irregular singularity, the normal form of fields of 1-resonant vectors and the classification theorem itself.

Reviewer: D.B.Gauld (Auckland)

MSC:

58D07	Groups and semigroups of nonlinear operators
55N30	Sheaf cohomology in algebraic topology
37A30	Ergodic theorems, spectral theory, Markov operators

Keywords:

vector fields; normal form; cohomology