Generic Antiholomorphic Polynomial Vector Fields

An analytic classification of generic anti-polynomial vector fields z = 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.