Bifurcations of certain family of planar vector fields tangent to axes

Abstract The topological versality of the family Vμ, x = x(μ 1 + x + y) , y = y(μ 2 + ax + by + cy 2 ) , of vector fields on the plane is proven. The asymptotic formulas of the bifurcational curves are given. The proofs rely on an analysis of the limit cycles and the non-abelian integrals along irrational curves.

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