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arXiv · 2407.03287

Generic Complex Polynomial Vector Fields with Real Coefficients

Jonathan Godin·Christiane Rousseau
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Abstract

The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a complete parametrization of these strata is given in terms of a modulus formed by a combinatorial and an analytic part. The bifurcation diagram is described for the degree 4. A realization theorem is proved for any generic modulus.

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Jonathan Godin, Christiane Rousseau. 2024-07-03. Generic Complex Polynomial Vector Fields with Real Coefficients. https://arxiv.org/abs/2407.03287

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