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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Semi-complete vector fields of saddle-node type in $\mathbb {C}^n$
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by Helena Reis PDF
Trans. Amer. Math. Soc. 360 (2008), 6611-6630 Request permission


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
  • Email:
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 6611-6630
  • MSC (2000): Primary 32S65
  • DOI:
  • MathSciNet review: 2434302