Generic reversible complex polynomial vector fields

2024/11/14 by Christiane Rousseau, Rousseau, Christiane
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2411.09108

openalex publication_date 2024/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper studies the generic complex 1-dimensional polynomial vector fields of the form iP(z)(∂)/(∂ 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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