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Topological classification of generic real rational functions

Sergei Natanzon·Boris Shapiro·Alek Vainshtein
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Abstract

To any real rational function with generic ramification points we assign a combinatorial object, called a garden, which consists of a weighted labeled directed planar chord diagram and of a set of weighted rooted trees each corresponding to a face of the diagram. We prove that any garden corresponds to a generic real rational function, and that equivalent functions have equivalent gardens.

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Sergei Natanzon, Boris Shapiro, Alek Vainshtein. 2001-10-21. Topological classification of generic real rational functions. https://arxiv.org/abs/math/0110235

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