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Zbl 0988.37066
Voronin, S.M.; Grintchy, A.A.
An analytic classification of saddle resonant singular points of holomorphic vector fields in the complex plane. (English)
[J] J. Dyn. Control Syst. 2, No.1, 21-53 (1996). ISSN 1079-2724; ISSN 1573-8698/e

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).
[Zofia Denkowska (Angers)]

MSC 2000:: *37G15 Bifurcations of limit cycles and periodic orbits
34C05 Qualitative theory of some special solutions of ODE
34C20 Transformation of ODE and systems
37G05 Normal forms

Keywords: analytic classification; saddle resonant singular points; holomorphic vector fields; $t$-monodromy

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