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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

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Source Normalized Impact per Paper (SNIP) 2018: 0.964

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Volume 17, Issue 3


Complete polynomial vector fields in two complex variables

Dominique Cerveau / Bruno Scárdua
  • Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, CEP. 21945-970 Rio de Janeiro—RJ, Brasil.
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Published Online: 2005-07-27 | DOI: https://doi.org/10.1515/form.2005.17.3.407


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 ℂ. For the case the generic orbit is diffeomorphic to ℂ ∖ {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.

About the article

Received: 20 March 2003

Published Online: 2005-07-27

Published in Print: 2005-05-25

Citation Information: Forum Mathematicum, Volume 17, Issue 3, Pages 407–430, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2005.17.3.407.

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