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Generic reversible complex polynomial vector fields

Dynamical Systems 2024-11-15 v1

Abstract

The paper studies the generic complex 1-dimensional polynomial vector fields of the form iP(z)ziP(z)\frac{\partial}{\partial z}, where PP 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.

Keywords

Cite

@article{arxiv.2411.09108,
  title  = {Generic reversible complex polynomial vector fields},
  author = {Christiane Rousseau},
  journal= {arXiv preprint arXiv:2411.09108},
  year   = {2024}
}

Comments

20 pages, 11 figures, one table