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Remarks about saddle-node bifurcation in the complex domain. (Remarques sur la bifurcation nœud-col dans le domaine complexe.) (French) Zbl 0655.58025

Singularités d’équations différentielles, Journ. Dijon/France 1985, Astérisque 150-151, 131-149 (1987).
[For the entire collection see Zbl 0623.00011.]
For a local diffeomorphism of \(\mathbb C\) at 0 tangent to the identity mapping the author gives the geometrical interpretation of Écalle’s analytic invariants using the global dynamics of infinitely close hyperbolic diffeomorphisms. The results of B. Malgrange [Sémin. Bourbaki, Vol. 24, 34e année (1981/1982), Exp. No. 582, Astérisque 92-93, 59–73 (1982; Zbl 0526.58009)] and S. M. Voronin [Funct. Anal. Appl. 15, 1–13 (1981); translation from Funkts. Anal. Prilozh. 15, No. 1, 1–17 (1981; Zbl 0463.30010)] are used.
Reviewer: B. V. Loginov

MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
37C80 Symmetries, equivariant dynamical systems (MSC2010)
58C25 Differentiable maps on manifolds