2018/11/03 by Kazumasa Inaba, Inaba, Kazumasa
Mathematics · #Advanced Differential Equations and Dynamical Systems #Meromorphic and Entire Functions #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1811.01189
Let f be a 1-variable complex polynomial such that f has a singularity at the origin. In the present paper, we show that there exists a deformation of f which has only fold singularities and cusps as singularities of a real polynomial map from the plane to the plane. We then calculate the number of cusps of a deformation in a sufficiently small neighborhood of the origin.