Desingularization of nilpotent singularities in families of planar vector fields
About this Title
Publication: Memoirs of the American Mathematical Society
Publication Year 2002: Volume 158, Number 753
ISBNs: 978-0-8218-2927-1 (print); 978-1-4704-0346-1 (online)
MathSciNet review: 1903719
MSC: Primary 34C05; Secondary 34C10, 34C23, 34E15, 37G99
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
- 1. Introduction
- 2. Background material
- 3. Nilpotent families and trivialization
- 4. Desingularization of nilpotent singularities
- 5. The proof of the desingularization theorem
- 6. Applications