Martinet, Jean 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 Cited in 5 Documents MSC: 37G99 Local and nonlocal bifurcation theory for dynamical systems 37C80 Symmetries, equivariant dynamical systems (MSC2010) 58C25 Differentiable maps on manifolds Keywords:saddle-node bifurcation; local diffeomorphism of C Citations:Zbl 0623.00011; Zbl 0526.58009; Zbl 0463.30010 PDFBibTeX XML