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arXiv · 2411.09108

Generic reversible complex polynomial vector fields

Christiane Rousseau
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Abstract

The paper studies the generic complex 1-dimensional polynomial vector fields of the form $iP(z)\frac{\partial}{\partial z}$, where $P$ is a polynomial 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 the strata is given in terms of a modulus formed by a combinatorial part and an analytic part. The bifurcation diagram is described for degrees 3 and 4. A realization theorem is proved for any generic modulus.

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Christiane Rousseau. 2024-11-14. Generic reversible complex polynomial vector fields. https://arxiv.org/abs/2411.09108

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