The dynamics of maps tangent to the identity and with non-vanishing\n index

2005/01/29 by Laura Molino, Molino, Laura
Mathematics · #32H50 #37F10 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.math/0501537

openalex publication_date 2005/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a germ of holomorphic self-map of C² at the origin O tangent to the\nidentity, and with O as a non-dicritical isolated fixed point. A parabolic\ncurve for f is a holomorphic f-invariant curve, with O on the boundary,\nattracted by O under the action of f. It has been shown that if the\ncharacteristic direction [v] has residual index not belonging to Q⁺, then\nthere exist parabolic curves for f tangent to [v]. In this paper we prove, with\na different method, that the conclusion still holds just assuming that the\nresidual index is not vanishing (at least when f is regular along [v]).\n

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