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Transactions of the American Mathematical Society

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Semi-complete vector fields of saddle-node type in $\mathbb {C}^n$

Author: Helena Reis
Journal: Trans. Amer. Math. Soc. 360 (2008), 6611-6630
MSC (2000): Primary 32S65
Published electronically: July 24, 2008
MathSciNet review: 2434302
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Abstract: We classify the foliations associated to codimension $1$ saddle-node vector fields on $\mathbb {C}^n$, with an isolated singularity, admitting a semi-complete representative. This will be done under some further assumptions that are generic in dimension $3$. These singularities play an essential role in the program to classify semi-complete vector fields in dimension $3$.

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Additional Information

Helena Reis
Affiliation: Centro de Matemática da Universidade do Porto, Faculdade de Economia da Universidade do Porto, Porto, Portugal

Received by editor(s): March 16, 2005
Received by editor(s) in revised form: March 5, 2007
Published electronically: July 24, 2008
Additional Notes: The author received financial support from Fundação para a Ciência e Tecnologia (FCT) through Centro de Matemática da Universidade do Porto, and from PRODEPIII
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.