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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

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 17, Issue 3

Issues

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

Abstract

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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Citing Articles

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[1]
T. Ito, B. Scárdua, and Y. Yamagishi
International Journal of Mathematics, 2014, Volume 25, Number 10, Page 1450093
[2]
Bruno Scárdua
Complex Variables and Elliptic Equations, 2007, Volume 52, Number 1, Page 79
[3]
BRUNO SCÁRDUA
Bulletin of the Australian Mathematical Society, 2010, Volume 82, Number 02, Page 177

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