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arXiv · 2503.01023

Generic Antiholomorphic Polynomial Vector Fields

Jonathan Godin·Jérémy Perazzelli
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Abstract

An analytic classification of generic anti-polynomial vector fields $\dot z = \overline{P(z)}$ is given in term of a topological and an analytic invariants. The number of generic strata in the parameter space is counted for each degree of $P$. A Realization Theorem is established for each pair of topological and analytic invariants. The non-generic case of a maximal number of heteroclinic connections is also given a classification. The bifurcation diagram for the quadratic case is presented.

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Jonathan Godin, Jérémy Perazzelli. 2025-05-16. Generic Antiholomorphic Polynomial Vector Fields. https://arxiv.org/abs/2503.01023

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