Analytic Invariants for Real-Analytic Germs of Vector Fields in (R², 0)

This article deals with two problems related with germs of foliations induced by real–analytic vector fields in (R ²,0) having singularity at 0 of order n, n≥ 2 . We will denote this class of vector fields by Aₙ . The goal of the first problem is to obtain a set of real–analytic invariants, called real–analytic Thom’s invariants, that allow us to achieve the real–analytic classification of vector fields satisfying genericity assumptions in a subclass A⁰ₙ of Aₙ . The second problem we deal with is called the realization problem, which consists in constructing a real analytic vector field having as real–analytic invariants a suitable group G of conformal mappings and a collection \α ᵢⱼ\ of $$(n-3)(n-2)/2$$ real constants that are given in advance.