An analytic classification of saddle resonant singular points of holomorphic vector fields in the complex plane (Q1972707)

It is impossible to resume this very rich work in a few words, especially as it uses advanced techniques elaborated by Arnold, Il'yashenko, Elizarov, Ecalle, Martinet, Ramis and others. As the authors put it, an analytic classification of general saddle resonant singular points of holomorphic vector fields in the plane is obtained and it is shown that this classification has two functional moduli more than an analytic orbital classification. All the elements needed to understand the paper are included (for instance the connection between the analytic and the orbital analytic classification). The problem of classification is reduced, as it is often the case, to the probelm of analytic classification of \(t\)-monodromy transformations (Theorem 5).