Combinatorial study of morsifications of real univariate singularities

Abstract

We study a broad class of morsifications of germs of univariate real analytic functions. We characterize the combinatorial types of the resulting Morse functions, via planar contact trees constructed from Newton-Puiseux roots of the polar curves of the morsifications.

23 pages, 16 figures. Compared to the first version, we clarified some statements as well as Figure 1 and we added Example 6.4 and Remarks 6.8, 7.1. To appear in Mathematische Nachrichten

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