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On vector fields in C without a separatrix.

J. Olivares-Vázquez — 1992

Revista Matemática de la Universidad Complutense de Madrid

A family of germs at 0 of holomorphic vector fields in C without separatrices is constructed, with the aid of the blown-up foliation F in the blown-up manifold C. We impose conditions on the multiplicity and the linear part of F at its singular points (i.e., non-semisimplicity and certain nonresonancy), which are sufficient for the original vector field to be separatrix-free.

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