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Desingularization of Nilpotent Singularities in Families of Planar Vector Fields
Daniel Panazzolo, Instituto de Matemática e Estatística, São Paolo, Brazil

Memoirs of the American Mathematical Society
2002; 108 pp; softcover
Volume: 158
ISBN-10: 0-8218-2927-0
ISBN-13: 978-0-8218-2927-1
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/158/753
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In this work, we prove a desingularization theorem for analytic families of two-dimensional vector fields, under the hypothesis that all its singularities have a non-vanishing first jet. Application to problems of Singular Perturbations and Finite Cyclicity are discussed in the last chapter.


Graduate students and research mathematicians interested in several complex variables and analytic spaces.

Table of Contents

  • Introduction
  • Background material
  • Nilpotent families and trivialization
  • Desingularization of Nilpotent singularities
  • The proof of the desingularization theorem
  • Applications
  • Bibliography
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