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Dominique Cerveau, Bruno Scárdua

Complete polynomial vector fields in two complex variables

We study the classification of polynomial vector fields in two complex variables under the hypotheses that the singularities are isolated and the flow is complete. Normal forms are obtained for the case the generic orbit is diffeomorphic to ?. For the case the generic orbit is diffeomorphic to ? ? {0} and there is an affine singularity we classify the linear part of the vector field and prove the existence of entire linearization or first integral.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 17, 05/2005
Pages: 407 - 430

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