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Absolutely isolated singularities of a differential equation

Published online by Cambridge University Press:  04 December 2007

F. SANCHO DE SALAS  and
P. SANCHO DE SALAS
F. SANCHO DE SALAS
Affiliation:
Department de Matemática Pura y Aplicada, Universidad de Salamanca, Plaza de la Merced 1–4, E-37008 Salamanca, Spain
P. SANCHO DE SALAS
Affiliation:
Department de Matemáticas, Universidad de Extremadura, Avda. de Elvas s/n, Badajoz, Spain
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Abstract

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In this paper we solve the problem of desingularization of an absolutely isolated singularity of a differential equation, including the dicritical case. As an application, we prove the finiteness of the number of dicritical points in the blowing up tree of an absolutely isolated singularity.

Keywords

Isolated singularitiesvector fieldsdesingularization
Type
Research Article
Information
Compositio Mathematica , Volume 106 , Issue 2 , April 1997 , pp. 235 - 246
Copyright
© 1997 Kluwer Academic Publishers